Daily Papers

Recent advances in text-guided image editing enable users to perform image edits through simple text inputs, leveraging the extensive priors of multi-step diffusion-based text-to-image models. However, these methods often fall short of the speed demands required for real-world and on-device applications due to the costly multi-step inversion and sampling process involved. In response to this, we introduce SwiftEdit, a simple yet highly efficient editing tool that achieve instant text-guided image editing (in 0.23s). The advancement of SwiftEdit lies in its two novel contributions: a one-step inversion framework that enables one-step image reconstruction via inversion and a mask-guided editing technique with our proposed attention rescaling mechanism to perform localized image editing. Extensive experiments are provided to demonstrate the effectiveness and efficiency of SwiftEdit. In particular, SwiftEdit enables instant text-guided image editing, which is extremely faster than previous multi-step methods (at least 50 times faster) while maintain a competitive performance in editing results. Our project page is at: https://swift-edit.github.io/

Recent diffusion and flow matching models have demonstrated strong capabilities in image generation and editing by progressively removing noise through iterative sampling. While this enables flexible inversion for semantic-preserving edits, few-step sampling regimes suffer from poor forward process approximation, leading to degraded editing quality. Existing few-step inversion methods often rely on pretrained generators and auxiliary modules, limiting scalability and generalization across different architectures. To address these limitations, we propose BiFM (Bidirectional Flow Matching), a unified framework that jointly learns generation and inversion within a single model. BiFM directly estimates average velocity fields in both ``image to noise" and ``noise to image" directions, constrained by a shared instantaneous velocity field derived from either predefined schedules or pretrained multi-step diffusion models. Additionally, BiFM introduces a novel training strategy using continuous time-interval supervision, stabilized by a bidirectional consistency objective and a lightweight time-interval embedding. This bidirectional formulation also enables one-step inversion and can integrate seamlessly into popular diffusion and flow matching backbones. Across diverse image editing and generation tasks, BiFM consistently outperforms existing few-step approaches, achieving superior performance and editability.

We address the challenges of precise image inversion and disentangled image editing in the context of few-step diffusion models. We introduce an encoder based iterative inversion technique. The inversion network is conditioned on the input image and the reconstructed image from the previous step, allowing for correction of the next reconstruction towards the input image. We demonstrate that disentangled controls can be easily achieved in the few-step diffusion model by conditioning on an (automatically generated) detailed text prompt. To manipulate the inverted image, we freeze the noise maps and modify one attribute in the text prompt (either manually or via instruction based editing driven by an LLM), resulting in the generation of a new image similar to the input image with only one attribute changed. It can further control the editing strength and accept instructive text prompt. Our approach facilitates realistic text-guided image edits in real-time, requiring only 8 number of functional evaluations (NFEs) in inversion (one-time cost) and 4 NFEs per edit. Our method is not only fast, but also significantly outperforms state-of-the-art multi-step diffusion editing techniques.

Despite the impressive performance of diffusion models such as Stable Diffusion (SD) in image generation, their slow inference limits practical deployment. Recent works accelerate inference by distilling multi-step diffusion into one-step generators. To better understand the distillation mechanism, we analyze U-Net/DiT weight changes between one-step students and their multi-step teacher counterparts. Our analysis reveals that changes in weight direction significantly exceed those in weight norm, highlighting it as the key factor during distillation. Motivated by this insight, we propose the Low-rank Rotation of weight Direction (LoRaD), a parameter-efficient adapter tailored to one-step diffusion distillation. LoRaD is designed to model these structured directional changes using learnable low-rank rotation matrices. We further integrate LoRaD into Variational Score Distillation (VSD), resulting in Weight Direction-aware Distillation (WaDi)-a novel one-step distillation framework. WaDi achieves state-of-the-art FID scores on COCO 2014 and COCO 2017 while using only approximately 10% of the trainable parameters of the U-Net/DiT. Furthermore, the distilled one-step model demonstrates strong versatility and scalability, generalizing well to various downstream tasks such as controllable generation, relation inversion, and high-resolution synthesis.

Diffusion inversion is the problem of taking an image and a text prompt that describes it and finding a noise latent that would generate the image. Most current inversion techniques operate by approximately solving an implicit equation and may converge slowly or yield poor reconstructed images. Here, we formulate the problem as finding the roots of an implicit equation and design a method to solve it efficiently. Our solution is based on Newton-Raphson (NR), a well-known technique in numerical analysis. A naive application of NR may be computationally infeasible and tends to converge to incorrect solutions. We describe an efficient regularized formulation that converges quickly to a solution that provides high-quality reconstructions. We also identify a source of inconsistency stemming from prompt conditioning during the inversion process, which significantly degrades the inversion quality. To address this, we introduce a prompt-aware adjustment of the encoding, effectively correcting this issue. Our solution, Regularized Newton-Raphson Inversion, inverts an image within 0.5 sec for latent consistency models, opening the door for interactive image editing. We further demonstrate improved results in image interpolation and generation of rare objects.

In subsurface imaging, learning the mapping from velocity maps to seismic waveforms (forward problem) and waveforms to velocity (inverse problem) is important for several applications. While traditional techniques for solving forward and inverse problems are computationally prohibitive, there is a growing interest in leveraging recent advances in deep learning to learn the mapping between velocity maps and seismic waveform images directly from data. Despite the variety of architectures explored in previous works, several open questions still remain unanswered such as the effect of latent space sizes, the importance of manifold learning, the complexity of translation models, and the value of jointly solving forward and inverse problems. We propose a unified framework to systematically characterize prior research in this area termed the Generalized Forward-Inverse (GFI) framework, building on the assumption of manifolds and latent space translations. We show that GFI encompasses previous works in deep learning for subsurface imaging, which can be viewed as specific instantiations of GFI. We also propose two new model architectures within the framework of GFI: Latent U-Net and Invertible X-Net, leveraging the power of U-Nets for domain translation and the ability of IU-Nets to simultaneously learn forward and inverse translations, respectively. We show that our proposed models achieve state-of-the-art (SOTA) performance for forward and inverse problems on a wide range of synthetic datasets, and also investigate their zero-shot effectiveness on two real-world-like datasets. Our code is available at https://github.com/KGML-lab/Generalized-Forward-Inverse-Framework-for-DL4SI

Diffusion models excel in high-quality generation but suffer from slow inference due to iterative sampling. While recent methods have successfully transformed diffusion models into one-step generators, they neglect model size reduction, limiting their applicability in compute-constrained scenarios. This paper aims to develop small, efficient one-step diffusion models based on the powerful rectified flow framework, by exploring joint compression of inference steps and model size. The rectified flow framework trains one-step generative models using two operations, reflow and distillation. Compared with the original framework, squeezing the model size brings two new challenges: (1) the initialization mismatch between large teachers and small students during reflow; (2) the underperformance of naive distillation on small student models. To overcome these issues, we propose Annealing Reflow and Flow-Guided Distillation, which together comprise our SlimFlow framework. With our novel framework, we train a one-step diffusion model with an FID of 5.02 and 15.7M parameters, outperforming the previous state-of-the-art one-step diffusion model (FID=6.47, 19.4M parameters) on CIFAR10. On ImageNet 64times64 and FFHQ 64times64, our method yields small one-step diffusion models that are comparable to larger models, showcasing the effectiveness of our method in creating compact, efficient one-step diffusion models.

We propose iterative inversion -- an algorithm for learning an inverse function without input-output pairs, but only with samples from the desired output distribution and access to the forward function. The key challenge is a distribution shift between the desired outputs and the outputs of an initial random guess, and we prove that iterative inversion can steer the learning correctly, under rather strict conditions on the function. We apply iterative inversion to learn control. Our input is a set of demonstrations of desired behavior, given as video embeddings of trajectories (without actions), and our method iteratively learns to imitate trajectories generated by the current policy, perturbed by random exploration noise. Our approach does not require rewards, and only employs supervised learning, which can be easily scaled to use state-of-the-art trajectory embedding techniques and policy representations. Indeed, with a VQ-VAE embedding, and a transformer-based policy, we demonstrate non-trivial continuous control on several tasks. Further, we report an improved performance on imitating diverse behaviors compared to reward based methods.

In Federated Learning (FL) and many other distributed training frameworks, collaborators can hold their private data locally and only share the network weights trained with the local data after multiple iterations. Gradient inversion is a family of privacy attacks that recovers data from its generated gradients. Seemingly, FL can provide a degree of protection against gradient inversion attacks on weight updates, since the gradient of a single step is concealed by the accumulation of gradients over multiple local iterations. In this work, we propose a principled way to extend gradient inversion attacks to weight updates in FL, thereby better exposing weaknesses in the presumed privacy protection inherent in FL. In particular, we propose a surrogate model method based on the characteristic of two-dimensional gradient flow and low-rank property of local updates. Our method largely boosts the ability of gradient inversion attacks on weight updates containing many iterations and achieves state-of-the-art (SOTA) performance. Additionally, our method runs up to 100times faster than the SOTA baseline in the common FL scenario. Our work re-evaluates and highlights the privacy risk of sharing network weights. Our code is available at https://github.com/JunyiZhu-AI/surrogate_model_extension.

When solving inverse problems, it is increasingly popular to use pre-trained diffusion models as plug-and-play priors. This framework can accommodate different forward models without re-training while preserving the generative capability of diffusion models. Despite their success in many imaging inverse problems, most existing methods rely on privileged information such as derivative, pseudo-inverse, or full knowledge about the forward model. This reliance poses a substantial limitation that restricts their use in a wide range of problems where such information is unavailable, such as in many scientific applications. To address this issue, we propose Ensemble Kalman Diffusion Guidance (EnKG) for diffusion models, a derivative-free approach that can solve inverse problems by only accessing forward model evaluations and a pre-trained diffusion model prior. We study the empirical effectiveness of our method across various inverse problems, including scientific settings such as inferring fluid flows and astronomical objects, which are highly non-linear inverse problems that often only permit black-box access to the forward model.

Recently, various methods have been proposed to address the inconsistency issue of DDIM inversion to enable image editing, such as EDICT [36] and Null-text inversion [22]. However, the above methods introduce considerable computational overhead. In this paper, we propose a new technique, named bi-directional integration approximation (BDIA), to perform exact diffusion inversion with neglible computational overhead. Suppose we would like to estimate the next diffusion state z_{i-1} at timestep t_i with the historical information (i,z_i) and (i+1,z_{i+1}). We first obtain the estimated Gaussian noise boldsymbol{epsilon}(z_i,i), and then apply the DDIM update procedure twice for approximating the ODE integration over the next time-slot [t_i, t_{i-1}] in the forward manner and the previous time-slot [t_i, t_{t+1}] in the backward manner. The DDIM step for the previous time-slot is used to refine the integration approximation made earlier when computing z_i. A nice property of BDIA-DDIM is that the update expression for z_{i-1} is a linear combination of (z_{i+1}, z_i, boldsymbol{epsilon}(z_i,i)). This allows for exact backward computation of z_{i+1} given (z_i, z_{i-1}), thus leading to exact diffusion inversion. It is demonstrated with experiments that (round-trip) BDIA-DDIM is particularly effective for image editing. Our experiments further show that BDIA-DDIM produces markedly better image sampling qualities than DDIM for text-to-image generation. BDIA can also be applied to improve the performance of other ODE solvers in addition to DDIM. In our work, it is found that applying BDIA to the EDM sampling procedure produces consistently better performance over four pre-trained models.

Recent advances in image editing with diffusion models have achieved impressive results, offering fine-grained control over the generation process. However, these methods are computationally intensive because of their iterative nature. While distilled diffusion models enable faster inference, their editing capabilities remain limited, primarily because of poor inversion quality. High-fidelity inversion and reconstruction are essential for precise image editing, as they preserve the structural and semantic integrity of the source image. In this work, we propose a novel framework that enhances image inversion using consistency models, enabling high-quality editing in just four steps. Our method introduces a cycle-consistency optimization strategy that significantly improves reconstruction accuracy and enables a controllable trade-off between editability and content preservation. We achieve state-of-the-art performance across various image editing tasks and datasets, demonstrating that our method matches or surpasses full-step diffusion models while being substantially more efficient. The code of our method is available on GitHub at https://github.com/ControlGenAI/Inverse-and-Edit.

Normalizing Flows (NFs) have been established as a principled framework for generative modeling. Standard NFs consist of a forward process and a reverse process: the forward process maps data to noise, while the reverse process generates samples by inverting it. Typical NF forward transformations are constrained by explicit invertibility, ensuring that the reverse process can serve as their exact analytic inverse. Recent developments in TARFlow and its variants have revitalized NF methods by combining Transformers and autoregressive flows, but have also exposed causal decoding as a major bottleneck. In this work, we introduce Bidirectional Normalizing Flow (BiFlow), a framework that removes the need for an exact analytic inverse. BiFlow learns a reverse model that approximates the underlying noise-to-data inverse mapping, enabling more flexible loss functions and architectures. Experiments on ImageNet demonstrate that BiFlow, compared to its causal decoding counterpart, improves generation quality while accelerating sampling by up to two orders of magnitude. BiFlow yields state-of-the-art results among NF-based methods and competitive performance among single-evaluation ("1-NFE") methods. Following recent encouraging progress on NFs, we hope our work will draw further attention to this classical paradigm.

In this paper, we unify more than 10 existing one-step diffusion distillation approaches, such as Diff-Instruct, DMD, SIM, SiD, f-distill, etc, inside a theory-driven framework which we name the \emph{Uni-Instruct}. Uni-Instruct is motivated by our proposed diffusion expansion theory of the f-divergence family. Then we introduce key theories that overcome the intractability issue of the original expanded f-divergence, resulting in an equivalent yet tractable loss that effectively trains one-step diffusion models by minimizing the expanded f-divergence family. The novel unification introduced by Uni-Instruct not only offers new theoretical contributions that help understand existing approaches from a high-level perspective but also leads to state-of-the-art one-step diffusion generation performances. On the CIFAR10 generation benchmark, Uni-Instruct achieves record-breaking Frechet Inception Distance (FID) values of \emph{1.46} for unconditional generation and \emph{1.38} for conditional generation. On the ImageNet-64times 64 generation benchmark, Uni-Instruct achieves a new SoTA one-step generation FID of \emph{1.02}, which outperforms its 79-step teacher diffusion with a significant improvement margin of 1.33 (1.02 vs 2.35). We also apply Uni-Instruct on broader tasks like text-to-3D generation. For text-to-3D generation, Uni-Instruct gives decent results, which slightly outperforms previous methods, such as SDS and VSD, in terms of both generation quality and diversity. Both the solid theoretical and empirical contributions of Uni-Instruct will potentially help future studies on one-step diffusion distillation and knowledge transferring of diffusion models.

Machine unlearning methods seek to revise pretrained models such that effects of certain training samples can be removed. In addition to effective erasure, low computational cost and general utility retention are also highly desirable. Existing unlearning methods usually involve iterative updates over the model parameters, which incurs a high computational cost. In this work, we propose an efficient method that only requires a one-time gradient computation, with which we modify only a single layer of model parameters. Specifically, we first identify a small number of model layers that lie on the Pareto front of high forget importance and low retain influence as critical layers. Then we search for a suitable step size and take a step along the gradient direction of a single critical layer while keeping other layers frozen. This method is highly modular and can be used to unlearn multiple concepts simultaneously in a controllable manner. We demonstrate the effectiveness and efficiency of this method on various models including CLIP, stable diffusion, and VLMs, surpassing other state-of-the-art methods.

We introduce a fully 3D, deep learning-based approach for the joint inversion of time-lapse surface gravity and seismic data for reconstructing subsurface density and velocity models. The target application of this proposed inversion approach is the prediction of subsurface CO2 plumes as a complementary tool for monitoring CO2 sequestration deployments. Our joint inversion technique outperforms deep learning-based gravity-only and seismic-only inversion models, achieving improved density and velocity reconstruction, accurate segmentation, and higher R-squared coefficients. These results indicate that deep learning-based joint inversion is an effective tool for CO_2 storage monitoring. Future work will focus on validating our approach with larger datasets, simulations with other geological storage sites, and ultimately field data.

Recent text-guided diffusion models provide powerful image generation capabilities. Currently, a massive effort is given to enable the modification of these images using text only as means to offer intuitive and versatile editing. To edit a real image using these state-of-the-art tools, one must first invert the image with a meaningful text prompt into the pretrained model's domain. In this paper, we introduce an accurate inversion technique and thus facilitate an intuitive text-based modification of the image. Our proposed inversion consists of two novel key components: (i) Pivotal inversion for diffusion models. While current methods aim at mapping random noise samples to a single input image, we use a single pivotal noise vector for each timestamp and optimize around it. We demonstrate that a direct inversion is inadequate on its own, but does provide a good anchor for our optimization. (ii) NULL-text optimization, where we only modify the unconditional textual embedding that is used for classifier-free guidance, rather than the input text embedding. This allows for keeping both the model weights and the conditional embedding intact and hence enables applying prompt-based editing while avoiding the cumbersome tuning of the model's weights. Our Null-text inversion, based on the publicly available Stable Diffusion model, is extensively evaluated on a variety of images and prompt editing, showing high-fidelity editing of real images.

Language model inversion seeks to recover hidden prompts using only language model outputs. This capability has implications for security and accountability in language model deployments, such as leaking private information from an API-protected language model's system message. We propose a new method -- prompt inversion from logprob sequences (PILS) -- that recovers hidden prompts by gleaning clues from the model's next-token probabilities over the course of multiple generation steps. Our method is enabled by a key insight: The vector-valued outputs of a language model occupy a low-dimensional subspace. This enables us to losslessly compress the full next-token probability distribution over multiple generation steps using a linear map, allowing more output information to be used for inversion. Our approach yields massive gains over previous state-of-the-art methods for recovering hidden prompts, achieving 2--3.5 times higher exact recovery rates across test sets, in one case increasing the recovery rate from 17% to 60%. Our method also exhibits surprisingly good generalization behavior; for instance, an inverter trained on 16 generations steps gets 5--27 points higher prompt recovery when we increase the number of steps to 32 at test time. Furthermore, we demonstrate strong performance of our method on the more challenging task of recovering hidden system messages. We also analyze the role of verbatim repetition in prompt recovery and propose a new method for cross-family model transfer for logit-based inverters. Our findings show that next-token probabilities are a considerably more vulnerable attack surface for inversion attacks than previously known.

Finding an initial noise vector that produces an input image when fed into the diffusion process (known as inversion) is an important problem in denoising diffusion models (DDMs), with applications for real image editing. The state-of-the-art approach for real image editing with inversion uses denoising diffusion implicit models (DDIMs) to deterministically noise the image to the intermediate state along the path that the denoising would follow given the original conditioning. However, DDIM inversion for real images is unstable as it relies on local linearization assumptions, which result in the propagation of errors, leading to incorrect image reconstruction and loss of content. To alleviate these problems, we propose Exact Diffusion Inversion via Coupled Transformations (EDICT), an inversion method that draws inspiration from affine coupling layers. EDICT enables mathematically exact inversion of real and model-generated images by maintaining two coupled noise vectors which are used to invert each other in an alternating fashion. Using Stable Diffusion, a state-of-the-art latent diffusion model, we demonstrate that EDICT successfully reconstructs real images with high fidelity. On complex image datasets like MS-COCO, EDICT reconstruction significantly outperforms DDIM, improving the mean square error of reconstruction by a factor of two. Using noise vectors inverted from real images, EDICT enables a wide range of image edits--from local and global semantic edits to image stylization--while maintaining fidelity to the original image structure. EDICT requires no model training/finetuning, prompt tuning, or extra data and can be combined with any pretrained DDM. Code is available at https://github.com/salesforce/EDICT.

We develop a unified theoretical framework for sparse knowledge distillation based on probability-domain softening operators. While the equivalence p^{1/T} propto softmax(z/T) is well known, our contribution is an operator-level analytical framework built on this foundation rather than the equivalence itself. The framework comprises four core components: (i) operator-agnostic bias--variance decompositions that characterize when sparse students outperform dense teachers, (ii) a homotopy path formalization of multi-stage pruning in function space explaining why iterative compression succeeds where one-shot pruning fails, (iii) convergence guarantees establishing O(1/n) rates for n-stage distillation with explicit parameter dependence, and (iv) equivalence class characterizations identifying distinct probability-domain operators that yield identical student models under capacity constraints. We introduce an axiomatic definition of probability-domain softening operators based on ranking preservation, continuity, entropy monotonicity, identity, and boundary behavior, and show that multiple non-equivalent operator families satisfy these axioms. All learning-theoretic guarantees are shown to hold uniformly across this operator class, independent of implementation details. These results provide theoretical grounding for black-box teacher distillation, partial-access settings such as top-k truncation and text-only outputs, and privacy-preserving model compression.

Recent advancements in text-guided diffusion models have unlocked powerful image manipulation capabilities. However, applying these methods to real images necessitates the inversion of the images into the domain of the pretrained diffusion model. Achieving faithful inversion remains a challenge, particularly for more recent models trained to generate images with a small number of denoising steps. In this work, we introduce an inversion method with a high quality-to-operation ratio, enhancing reconstruction accuracy without increasing the number of operations. Building on reversing the diffusion sampling process, our method employs an iterative renoising mechanism at each inversion sampling step. This mechanism refines the approximation of a predicted point along the forward diffusion trajectory, by iteratively applying the pretrained diffusion model, and averaging these predictions. We evaluate the performance of our ReNoise technique using various sampling algorithms and models, including recent accelerated diffusion models. Through comprehensive evaluations and comparisons, we show its effectiveness in terms of both accuracy and speed. Furthermore, we confirm that our method preserves editability by demonstrating text-driven image editing on real images.

We present StableMotion, a novel framework leverages knowledge (geometry and content priors) from pretrained large-scale image diffusion models to perform motion estimation, solving single-image-based image rectification tasks such as Stitched Image Rectangling (SIR) and Rolling Shutter Correction (RSC). Specifically, StableMotion framework takes text-to-image Stable Diffusion (SD) models as backbone and repurposes it into an image-to-motion estimator. To mitigate inconsistent output produced by diffusion models, we propose Adaptive Ensemble Strategy (AES) that consolidates multiple outputs into a cohesive, high-fidelity result. Additionally, we present the concept of Sampling Steps Disaster (SSD), the counterintuitive scenario where increasing the number of sampling steps can lead to poorer outcomes, which enables our framework to achieve one-step inference. StableMotion is verified on two image rectification tasks and delivers state-of-the-art performance in both, as well as showing strong generalizability. Supported by SSD, StableMotion offers a speedup of 200 times compared to previous diffusion model-based methods.

Recent advances in few-step diffusion models have demonstrated their efficiency and effectiveness by shortcutting the probabilistic paths of diffusion models, especially in training one-step diffusion models from scratch (a.k.a. shortcut models). However, their theoretical derivation and practical implementation are often closely coupled, which obscures the design space. To address this, we propose a common design framework for representative shortcut models. This framework provides theoretical justification for their validity and disentangles concrete component-level choices, thereby enabling systematic identification of improvements. With our proposed improvements, the resulting one-step model achieves a new state-of-the-art FID50k of 2.85 on ImageNet-256x256 under the classifier-free guidance setting with one step generation, and further reaches FID50k of 2.53 with 2x training steps. Remarkably, the model requires no pre-training, distillation, or curriculum learning. We believe our work lowers the barrier to component-level innovation in shortcut models and facilitates principled exploration of their design space.

The Inversion-Denoising Paradigm, which is based on diffusion models, excels in diverse image editing and restoration tasks. We revisit its mechanism and reveal a critical, overlooked factor in reconstruction degradation: the approximate noise error. This error stems from approximating the noise at step t with the prediction at step t-1, resulting in severe error accumulation throughout the inversion process. We introduce Projection-Orthogonal Least Squares for Robust and Adaptive Inversion (POLARIS), which reformulates inversion from an error-compensation problem into an error-origin problem. Rather than optimizing embeddings or latent codes to offset accumulated drift, POLARIS treats the guidance scale ω as a step-wise variable and derives a mathematically grounded formula to minimize inversion error at each step. Remarkably, POLARIS improves inversion latent quality with just one line of code. With negligible performance overhead, it substantially mitigates noise approximation errors and consistently improves the accuracy of downstream tasks.

Model Inversion (MI) attacks aim to reconstruct information from private training data by exploiting access to machine learning models T. To evaluate such attacks, the standard evaluation framework relies on an evaluation model E, trained under the same task design as T. This framework has become the de facto standard for assessing progress in MI research, used across nearly all recent MI studies without question. In this paper, we present the first in-depth study of this evaluation framework. In particular, we identify a critical issue of this standard framework: Type-I adversarial examples. These are reconstructions that do not capture the visual features of private training data, yet are still deemed successful by T and ultimately transferable to E. Such false positives undermine the reliability of the standard MI evaluation framework. To address this issue, we introduce a new MI evaluation framework that replaces the evaluation model E with advanced Multimodal Large Language Models (MLLMs). By leveraging their general-purpose visual understanding, our MLLM-based framework does not depend on training of shared task design as in T, thus reducing Type-I transferability and providing more faithful assessments of reconstruction success. Using our MLLM-based evaluation framework, we reevaluate 27 diverse MI attack setups and empirically reveal consistently high false positive rates under the standard evaluation framework. Importantly, we demonstrate that many state-of-the-art (SOTA) MI methods report inflated attack accuracy, indicating that actual privacy leakage is significantly lower than previously believed. By uncovering this critical issue and proposing a robust solution, our work enables a reassessment of progress in MI research and sets a new standard for reliable and robust evaluation. Code can be found in https://github.com/hosytuyen/MI-Eval-MLLM

Despite all recent progress, it is still challenging to edit and manipulate natural images with modern generative models. When using Generative Adversarial Network (GAN), one major hurdle is in the inversion process mapping a real image to its corresponding noise vector in the latent space, since its necessary to be able to reconstruct an image to edit its contents. Likewise for Denoising Diffusion Implicit Models (DDIM), the linearization assumption in each inversion step makes the whole deterministic inversion process unreliable. Existing approaches that have tackled the problem of inversion stability often incur in significant trade-offs in computational efficiency. In this work we propose an Accelerated Iterative Diffusion Inversion method, dubbed AIDI, that significantly improves reconstruction accuracy with minimal additional overhead in space and time complexity. By using a novel blended guidance technique, we show that effective results can be obtained on a large range of image editing tasks without large classifier-free guidance in inversion. Furthermore, when compared with other diffusion inversion based works, our proposed process is shown to be more robust for fast image editing in the 10 and 20 diffusion steps' regimes.

We, team AImsterdam, summarize our submission to the fastMRI challenge (Zbontar et al., 2018). Our approach builds on recent advances in invertible learning to infer models as presented in Putzky and Welling (2019). Both, our single-coil and our multi-coil model share the same basic architecture.

Editing real images using a pre-trained text-to-image (T2I) diffusion/flow model often involves inverting the image into its corresponding noise map. However, inversion by itself is typically insufficient for obtaining satisfactory results, and therefore many methods additionally intervene in the sampling process. Such methods achieve improved results but are not seamlessly transferable between model architectures. Here, we introduce FlowEdit, a text-based editing method for pre-trained T2I flow models, which is inversion-free, optimization-free and model agnostic. Our method constructs an ODE that directly maps between the source and target distributions (corresponding to the source and target text prompts) and achieves a lower transport cost than the inversion approach. This leads to state-of-the-art results, as we illustrate with Stable Diffusion 3 and FLUX. Code and examples are available on the project's webpage.

Despite recent advances in inversion-based editing, text-guided image manipulation remains challenging for diffusion models. The primary bottlenecks include 1) the time-consuming nature of the inversion process; 2) the struggle to balance consistency with accuracy; 3) the lack of compatibility with efficient consistency sampling methods used in consistency models. To address the above issues, we start by asking ourselves if the inversion process can be eliminated for editing. We show that when the initial sample is known, a special variance schedule reduces the denoising step to the same form as the multi-step consistency sampling. We name this Denoising Diffusion Consistent Model (DDCM), and note that it implies a virtual inversion strategy without explicit inversion in sampling. We further unify the attention control mechanisms in a tuning-free framework for text-guided editing. Combining them, we present inversion-free editing (InfEdit), which allows for consistent and faithful editing for both rigid and non-rigid semantic changes, catering to intricate modifications without compromising on the image's integrity and explicit inversion. Through extensive experiments, InfEdit shows strong performance in various editing tasks and also maintains a seamless workflow (less than 3 seconds on one single A40), demonstrating the potential for real-time applications. Project Page: https://sled-group.github.io/InfEdit/

Model Inversion (MI) attacks aim to reconstruct private training data by abusing access to machine learning models. Contemporary MI attacks have achieved impressive attack performance, posing serious threats to privacy. Meanwhile, all existing MI defense methods rely on regularization that is in direct conflict with the training objective, resulting in noticeable degradation in model utility. In this work, we take a different perspective, and propose a novel and simple Transfer Learning-based Defense against Model Inversion (TL-DMI) to render MI-robust models. Particularly, by leveraging TL, we limit the number of layers encoding sensitive information from private training dataset, thereby degrading the performance of MI attack. We conduct an analysis using Fisher Information to justify our method. Our defense is remarkably simple to implement. Without bells and whistles, we show in extensive experiments that TL-DMI achieves state-of-the-art (SOTA) MI robustness. Our code, pre-trained models, demo and inverted data are available at: https://hosytuyen.github.io/projects/TL-DMI

Rectified flow and reflow procedures have significantly advanced fast generation by progressively straightening ordinary differential equation (ODE) flows. They operate under the assumption that image and noise pairs, known as couplings, can be approximated by straight trajectories with constant velocity. However, we observe that modeling with constant velocity and using reflow procedures have limitations in accurately learning straight trajectories between pairs, resulting in suboptimal performance in few-step generation. To address these limitations, we introduce Constant Acceleration Flow (CAF), a novel framework based on a simple constant acceleration equation. CAF introduces acceleration as an additional learnable variable, allowing for more expressive and accurate estimation of the ODE flow. Moreover, we propose two techniques to further improve estimation accuracy: initial velocity conditioning for the acceleration model and a reflow process for the initial velocity. Our comprehensive studies on toy datasets, CIFAR-10, and ImageNet 64x64 demonstrate that CAF outperforms state-of-the-art baselines for one-step generation. We also show that CAF dramatically improves few-step coupling preservation and inversion over Rectified flow. Code is available at https://github.com/mlvlab/CAF{https://github.com/mlvlab/CAF}.

Generative models transform random noise into images; their inversion aims to transform images back to structured noise for recovery and editing. This paper addresses two key tasks: (i) inversion and (ii) editing of a real image using stochastic equivalents of rectified flow models (such as Flux). Although Diffusion Models (DMs) have recently dominated the field of generative modeling for images, their inversion presents faithfulness and editability challenges due to nonlinearities in drift and diffusion. Existing state-of-the-art DM inversion approaches rely on training of additional parameters or test-time optimization of latent variables; both are expensive in practice. Rectified Flows (RFs) offer a promising alternative to diffusion models, yet their inversion has been underexplored. We propose RF inversion using dynamic optimal control derived via a linear quadratic regulator. We prove that the resulting vector field is equivalent to a rectified stochastic differential equation. Additionally, we extend our framework to design a stochastic sampler for Flux. Our inversion method allows for state-of-the-art performance in zero-shot inversion and editing, outperforming prior works in stroke-to-image synthesis and semantic image editing, with large-scale human evaluations confirming user preference.

State-space models (SSMs) have recently emerged as a framework for learning long-range sequence tasks. An example is the structured state-space sequence (S4) layer, which uses the diagonal-plus-low-rank structure of the HiPPO initialization framework. However, the complicated structure of the S4 layer poses challenges; and, in an effort to address these challenges, models such as S4D and S5 have considered a purely diagonal structure. This choice simplifies the implementation, improves computational efficiency, and allows channel communication. However, diagonalizing the HiPPO framework is itself an ill-posed problem. In this paper, we propose a general solution for this and related ill-posed diagonalization problems in machine learning. We introduce a generic, backward-stable "perturb-then-diagonalize" (PTD) methodology, which is based on the pseudospectral theory of non-normal operators, and which may be interpreted as the approximate diagonalization of the non-normal matrices defining SSMs. Based on this, we introduce the S4-PTD and S5-PTD models. Through theoretical analysis of the transfer functions of different initialization schemes, we demonstrate that the S4-PTD/S5-PTD initialization strongly converges to the HiPPO framework, while the S4D/S5 initialization only achieves weak convergences. As a result, our new models show resilience to Fourier-mode noise-perturbed inputs, a crucial property not achieved by the S4D/S5 models. In addition to improved robustness, our S5-PTD model averages 87.6% accuracy on the Long-Range Arena benchmark, demonstrating that the PTD methodology helps to improve the accuracy of deep learning models.

User data confidentiality protection is becoming a rising challenge in the present deep learning research. Without access to data, conventional data-driven model compression faces a higher risk of performance degradation. Recently, some works propose to generate images from a specific pretrained model to serve as training data. However, the inversion process only utilizes biased feature statistics stored in one model and is from low-dimension to high-dimension. As a consequence, it inevitably encounters the difficulties of generalizability and inexact inversion, which leads to unsatisfactory performance. To address these problems, we propose MixMix based on two simple yet effective techniques: (1) Feature Mixing: utilizes various models to construct a universal feature space for generalized inversion; (2) Data Mixing: mixes the synthesized images and labels to generate exact label information. We prove the effectiveness of MixMix from both theoretical and empirical perspectives. Extensive experiments show that MixMix outperforms existing methods on the mainstream compression tasks, including quantization, knowledge distillation, and pruning. Specifically, MixMix achieves up to 4% and 20% accuracy uplift on quantization and pruning, respectively, compared to existing data-free compression work.

Existing single image-to-3D creation methods typically involve a two-stage process, first generating multi-view images, and then using these images for 3D reconstruction. However, training these two stages separately leads to significant data bias in the inference phase, thus affecting the quality of reconstructed results. We introduce a unified 3D generation framework, named Ouroboros3D, which integrates diffusion-based multi-view image generation and 3D reconstruction into a recursive diffusion process. In our framework, these two modules are jointly trained through a self-conditioning mechanism, allowing them to adapt to each other's characteristics for robust inference. During the multi-view denoising process, the multi-view diffusion model uses the 3D-aware maps rendered by the reconstruction module at the previous timestep as additional conditions. The recursive diffusion framework with 3D-aware feedback unites the entire process and improves geometric consistency.Experiments show that our framework outperforms separation of these two stages and existing methods that combine them at the inference phase. Project page: https://costwen.github.io/Ouroboros3D/

State-of-the-art text-to-image models produce high-quality images, but inference remains expensive as generation requires several sequential ODE or denoising steps. Native one-step models aim to reduce this cost by mapping noise to an image in a single step, yet fair comparisons to multi-step systems are difficult because studies use mismatched sampling steps and different classifier-free guidance (CFG) settings, where CFG can shift FID, Inception Score, and CLIP-based alignment in opposing directions. It is also unclear how well one-step models scale to multi-step inference, and there is limited standardized out-of-distribution evaluation for label-ID-conditioned generators beyond ImageNet. To address this, We benchmark eight models spanning one-step flows (MeanFlow, Improved MeanFlow, SoFlow), multi-step baselines (RAE, Scale-RAE), and established systems (SiT, Stable Diffusion 3.5, FLUX.1) under a controlled class-conditional protocol on ImageNet validation, ImageNetV2, and reLAIONet, our new proofread out-of-distribution dataset aligned to ImageNet label IDs. Using FID, Inception Score, CLIP Score, and Pick Score, we show that FID-focused model development and CFG selection can be misleading in few-step regimes, where guidance changes can improve FID while degrading text-image alignment and human preference signals and worsening perceived quality. We further show that leading one-step models benefit from step scaling and become substantially more competitive under multi-step inference, although they still exhibit characteristic local distortions. To capture these tradeoffs, we introduce MinMax Harmonic Mean (MMHM), a composite proxy over all four metrics that stabilizes hyperparameter selection across guidance and step sweeps.

Text-guided diffusion models have revolutionized image generation and editing, offering exceptional realism and diversity. Specifically, in the context of diffusion-based editing, where a source image is edited according to a target prompt, the process commences by acquiring a noisy latent vector corresponding to the source image via the diffusion model. This vector is subsequently fed into separate source and target diffusion branches for editing. The accuracy of this inversion process significantly impacts the final editing outcome, influencing both essential content preservation of the source image and edit fidelity according to the target prompt. Prior inversion techniques aimed at finding a unified solution in both the source and target diffusion branches. However, our theoretical and empirical analyses reveal that disentangling these branches leads to a distinct separation of responsibilities for preserving essential content and ensuring edit fidelity. Building on this insight, we introduce "Direct Inversion," a novel technique achieving optimal performance of both branches with just three lines of code. To assess image editing performance, we present PIE-Bench, an editing benchmark with 700 images showcasing diverse scenes and editing types, accompanied by versatile annotations and comprehensive evaluation metrics. Compared to state-of-the-art optimization-based inversion techniques, our solution not only yields superior performance across 8 editing methods but also achieves nearly an order of speed-up.

Existing techniques for model inversion typically rely on hard-to-tune regularizers, such as total variation or feature regularization, which must be individually calibrated for each network in order to produce adequate images. In this work, we introduce Plug-In Inversion, which relies on a simple set of augmentations and does not require excessive hyper-parameter tuning. Under our proposed augmentation-based scheme, the same set of augmentation hyper-parameters can be used for inverting a wide range of image classification models, regardless of input dimensions or the architecture. We illustrate the practicality of our approach by inverting Vision Transformers (ViTs) and Multi-Layer Perceptrons (MLPs) trained on the ImageNet dataset, tasks which to the best of our knowledge have not been successfully accomplished by any previous works.

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

Recent advancements in video generation have spurred the development of video editing techniques, which can be divided into inversion-based and end-to-end methods. However, current video editing methods still suffer from several challenges. Inversion-based methods, though training-free and flexible, are time-consuming during inference, struggle with fine-grained editing instructions, and produce artifacts and jitter. On the other hand, end-to-end methods, which rely on edited video pairs for training, offer faster inference speeds but often produce poor editing results due to a lack of high-quality training video pairs. In this paper, to close the gap in end-to-end methods, we introduce Se\~norita-2M, a high-quality video editing dataset. Se\~norita-2M consists of approximately 2 millions of video editing pairs. It is built by crafting four high-quality, specialized video editing models, each crafted and trained by our team to achieve state-of-the-art editing results. We also propose a filtering pipeline to eliminate poorly edited video pairs. Furthermore, we explore common video editing architectures to identify the most effective structure based on current pre-trained generative model. Extensive experiments show that our dataset can help to yield remarkably high-quality video editing results. More details are available at https://senorita.github.io.

We study the estimation of a planted signal hidden in a recently introduced nested matrix-tensor model, which is an extension of the classical spiked rank-one tensor model, motivated by multi-view clustering. Prior work has theoretically examined the performance of a tensor-based approach, which relies on finding a best rank-one approximation, a problem known to be computationally hard. A tractable alternative approach consists in computing instead the best rank-one (matrix) approximation of an unfolding of the observed tensor data, but its performance was hitherto unknown. We quantify here the performance gap between these two approaches, in particular by deriving the precise algorithmic threshold of the unfolding approach and demonstrating that it exhibits a BBP-type transition behavior. This work is therefore in line with recent contributions which deepen our understanding of why tensor-based methods surpass matrix-based methods in handling structured tensor data.

Though Rectified Flows (ReFlows) with distillation offers a promising way for fast sampling, its fast inversion transforms images back to structured noise for recovery and following editing remains unsolved. This paper introduces FireFlow, a simple yet effective zero-shot approach that inherits the startling capacity of ReFlow-based models (such as FLUX) in generation while extending its capabilities to accurate inversion and editing in 8 steps. We first demonstrate that a carefully designed numerical solver is pivotal for ReFlow inversion, enabling accurate inversion and reconstruction with the precision of a second-order solver while maintaining the practical efficiency of a first-order Euler method. This solver achieves a 3times runtime speedup compared to state-of-the-art ReFlow inversion and editing techniques, while delivering smaller reconstruction errors and superior editing results in a training-free mode. The code is available at https://github.com/HolmesShuan/FireFlow{this URL}.

We consider the inverse problem of reconstructing the spatial layout of a place, a home floorplan for example, from a user`s movements inside that layout. Direct inversion is ill-posed since many floorplans can explain the same movement trajectories. We adopt a diffusion-based posterior sampler to generate layouts consistent with the measurements. While active research is in progress on generative inverse solvers, we find that the forward operator in our problem poses new challenges. The path-planning process inside a floorplan is a non-invertible, non-differentiable function, and causes instability while optimizing using the likelihood score. We break-away from existing approaches and reformulate the likelihood score in a smoother embedding space. The embedding space is trained with a contrastive loss which brings compatible floorplans and trajectories close to each other, while pushing mismatched pairs far apart. We show that a surrogate form of the likelihood score in this embedding space is a valid approximation of the true likelihood score, making it possible to steer the denoising process towards the posterior. Across extensive experiments, our model CoGuide produces more consistent floorplans from trajectories, and is more robust than differentiable-planner baselines and guided-diffusion methods.

It is well known that many open-released foundational diffusion models have difficulty in generating images that substantially depart from average brightness, despite such images being present in the training data. This is due to an inconsistency: while denoising starts from pure Gaussian noise during inference, the training noise schedule retains residual data even in the final timestep distribution, due to difficulties in numerical conditioning in mainstream formulation, leading to unintended bias during inference. To mitigate this issue, certain epsilon-prediction models are combined with an ad-hoc offset-noise methodology. In parallel, some contemporary models have adopted zero-terminal SNR noise schedules together with v-prediction, which necessitate major alterations to pre-trained models. However, such changes risk destabilizing a large multitude of community-driven applications anchored on these pre-trained models. In light of this, our investigation revisits the fundamental causes, leading to our proposal of an innovative and principled remedy, called One More Step (OMS). By integrating a compact network and incorporating an additional simple yet effective step during inference, OMS elevates image fidelity and harmonizes the dichotomy between training and inference, while preserving original model parameters. Once trained, various pre-trained diffusion models with the same latent domain can share the same OMS module.

This paper presents a video inversion approach for zero-shot video editing, which aims to model the input video with low-rank representation during the inversion process. The existing video editing methods usually apply the typical 2D DDIM inversion or na\"ive spatial-temporal DDIM inversion before editing, which leverages time-varying representation for each frame to derive noisy latent. Unlike most existing approaches, we propose a Spatial-Temporal Expectation-Maximization (STEM) inversion, which formulates the dense video feature under an expectation-maximization manner and iteratively estimates a more compact basis set to represent the whole video. Each frame applies the fixed and global representation for inversion, which is more friendly for temporal consistency during reconstruction and editing. Extensive qualitative and quantitative experiments demonstrate that our STEM inversion can achieve consistent improvement on two state-of-the-art video editing methods.

Diffusion model-based inverse problem solvers have shown impressive performance, but are limited in speed, mostly as they require reverse diffusion sampling starting from noise. Several recent works have tried to alleviate this problem by building a diffusion process, directly bridging the clean and the corrupted for specific inverse problems. In this paper, we first unify these existing works under the name Direct Diffusion Bridges (DDB), showing that while motivated by different theories, the resulting algorithms only differ in the choice of parameters. Then, we highlight a critical limitation of the current DDB framework, namely that it does not ensure data consistency. To address this problem, we propose a modified inference procedure that imposes data consistency without the need for fine-tuning. We term the resulting method data Consistent DDB (CDDB), which outperforms its inconsistent counterpart in terms of both perception and distortion metrics, thereby effectively pushing the Pareto-frontier toward the optimum. Our proposed method achieves state-of-the-art results on both evaluation criteria, showcasing its superiority over existing methods.

A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions. Existing operator learning frameworks map functions to functions and need to be modified to learn inverse maps from data. We propose a novel architecture termed Neural Inverse Operators (NIOs) to solve these PDE inverse problems. Motivated by the underlying mathematical structure, NIO is based on a suitable composition of DeepONets and FNOs to approximate mappings from operators to functions. A variety of experiments are presented to demonstrate that NIOs significantly outperform baselines and solve PDE inverse problems robustly, accurately and are several orders of magnitude faster than existing direct and PDE-constrained optimization methods.

While diffusion distillation has enabled one-step generation through methods like Variational Score Distillation, adapting distilled models to emerging new controls -- such as novel structural constraints or latest user preferences -- remains challenging. Conventional approaches typically requires modifying the base diffusion model and redistilling it -- a process that is both computationally intensive and time-consuming. To address these challenges, we introduce Joint Distribution Matching (JDM), a novel approach that minimizes the reverse KL divergence between image-condition joint distributions. By deriving a tractable upper bound, JDM decouples fidelity learning from condition learning. This asymmetric distillation scheme enables our one-step student to handle controls unknown to the teacher model and facilitates improved classifier-free guidance (CFG) usage and seamless integration of human feedback learning (HFL). Experimental results demonstrate that JDM surpasses baseline methods such as multi-step ControlNet by mere one-step in most cases, while achieving state-of-the-art performance in one-step text-to-image synthesis through improved usage of CFG or HFL integration.

Diffusion models (DMs) have significantly advanced the development of real-world image super-resolution (Real-ISR), but the computational cost of multi-step diffusion models limits their application. One-step diffusion models generate high-quality images in a one sampling step, greatly reducing computational overhead and inference latency. However, most existing one-step diffusion methods are constrained by the performance of the teacher model, where poor teacher performance results in image artifacts. To address this limitation, we propose FluxSR, a novel one-step diffusion Real-ISR technique based on flow matching models. We use the state-of-the-art diffusion model FLUX.1-dev as both the teacher model and the base model. First, we introduce Flow Trajectory Distillation (FTD) to distill a multi-step flow matching model into a one-step Real-ISR. Second, to improve image realism and address high-frequency artifact issues in generated images, we propose TV-LPIPS as a perceptual loss and introduce Attention Diversification Loss (ADL) as a regularization term to reduce token similarity in transformer, thereby eliminating high-frequency artifacts. Comprehensive experiments demonstrate that our method outperforms existing one-step diffusion-based Real-ISR methods. The code and model will be released at https://github.com/JianzeLi-114/FluxSR.

Diffusion models have achieved remarkable success in image generation and editing tasks. Inversion within these models aims to recover the latent noise representation for a real or generated image, enabling reconstruction, editing, and other downstream tasks. However, to date, most inversion approaches suffer from an intrinsic trade-off between reconstruction accuracy and editing flexibility. This limitation arises from the difficulty of maintaining both semantic alignment and structural consistency during the inversion process. In this work, we introduce Dual-Conditional Inversion (DCI), a novel framework that jointly conditions on the source prompt and reference image to guide the inversion process. Specifically, DCI formulates the inversion process as a dual-condition fixed-point optimization problem, minimizing both the latent noise gap and the reconstruction error under the joint guidance. This design anchors the inversion trajectory in both semantic and visual space, leading to more accurate and editable latent representations. Our novel setup brings new understanding to the inversion process. Extensive experiments demonstrate that DCI achieves state-of-the-art performance across multiple editing tasks, significantly improving both reconstruction quality and editing precision. Furthermore, we also demonstrate that our method achieves strong results in reconstruction tasks, implying a degree of robustness and generalizability approaching the ultimate goal of the inversion process.

We propose a principled and effective framework for one-step generative modeling. We introduce the notion of average velocity to characterize flow fields, in contrast to instantaneous velocity modeled by Flow Matching methods. A well-defined identity between average and instantaneous velocities is derived and used to guide neural network training. Our method, termed the MeanFlow model, is self-contained and requires no pre-training, distillation, or curriculum learning. MeanFlow demonstrates strong empirical performance: it achieves an FID of 3.43 with a single function evaluation (1-NFE) on ImageNet 256x256 trained from scratch, significantly outperforming previous state-of-the-art one-step diffusion/flow models. Our study substantially narrows the gap between one-step diffusion/flow models and their multi-step predecessors, and we hope it will motivate future research to revisit the foundations of these powerful models.

Reverse-mode differentiation is used for optimization, but it introduces references, which break the purity of the underlying programs, making them notoriously harder to optimize. We present a reverse-mode differentiation on a purely functional language with array operations. It is the first one to deliver a provably efficient, purely functional, and denotationally correct reverse-mode differentiation. We show that our transformation is semantically correct and verifies the cheap gradient principle. Inspired by PROPs and compilation to categories, we introduce a novel intermediate representation that we call 'unary form'. Our reverse-mode transformation is factored as a compilation scheme through this intermediate representation. We obtain provably efficient gradients by performing general partial evaluation optimizations after our reverse-mode transformation, as opposed to manually derived ones. For simple first-order programs, the obtained output programs resemble static-single-assignment (SSA) code. We emphasize the modularity of our approach and show how our language can easily be enriched with more optimized primitives, as required for some speed-ups in practice.

It is widely believed that the success of deep convolutional networks is based on progressively discarding uninformative variability about the input with respect to the problem at hand. This is supported empirically by the difficulty of recovering images from their hidden representations, in most commonly used network architectures. In this paper we show via a one-to-one mapping that this loss of information is not a necessary condition to learn representations that generalize well on complicated problems, such as ImageNet. Via a cascade of homeomorphic layers, we build the i-RevNet, a network that can be fully inverted up to the final projection onto the classes, i.e. no information is discarded. Building an invertible architecture is difficult, for one, because the local inversion is ill-conditioned, we overcome this by providing an explicit inverse. An analysis of i-RevNets learned representations suggests an alternative explanation for the success of deep networks by a progressive contraction and linear separation with depth. To shed light on the nature of the model learned by the i-RevNet we reconstruct linear interpolations between natural image representations.

Gradient inversion attacks aim to reconstruct local training data from intermediate gradients exposed in the federated learning framework. Despite successful attacks, all previous methods, starting from reconstructing a single data point and then relaxing the single-image limit to batch level, are only tested under hard label constraints. Even for single-image reconstruction, we still lack an analysis-based algorithm to recover augmented soft labels. In this work, we change the focus from enlarging batchsize to investigating the hard label constraints, considering a more realistic circumstance where label smoothing and mixup techniques are used in the training process. In particular, we are the first to initiate a novel algorithm to simultaneously recover the ground-truth augmented label and the input feature of the last fully-connected layer from single-input gradients, and provide a necessary condition for any analytical-based label recovery methods. Extensive experiments testify to the label recovery accuracy, as well as the benefits to the following image reconstruction. We believe soft labels in classification tasks are worth further attention in gradient inversion attacks.

Consistency-based generative models like Shortcut and MeanFlow achieve impressive results via a target-aware design for solving the Probability Flow ODE (PF-ODE). Typically, such methods introduce a target time r alongside the current time t to modulate outputs between a local multi-step derivative (r = t) and a global few-step integral (r = 0). However, the conventional "one input, one output" paradigm enforces a partition of the training budget, often allocating a significant portion (e.g., 75% in MeanFlow) solely to the multi-step objective for stability. This separation forces a trade-off: allocating sufficient samples to the multi-step objective leaves the few-step generation undertrained, which harms convergence and limits scalability. To this end, we propose Duality Models (DuMo) via a "one input, dual output" paradigm. Using a shared backbone with dual heads, DuMo simultaneously predicts velocity v_t and flow-map u_t from a single input x_t. This applies geometric constraints from the multi-step objective to every sample, bounding the few-step estimation without separating training objectives, thereby significantly improving stability and efficiency. On ImageNet 256 times 256, a 679M Diffusion Transformer with SD-VAE achieves a state-of-the-art (SOTA) FID of 1.79 in just 2 steps. Code is available at: https://github.com/LINs-lab/DuMo

Diffusion model-based inverse problem solvers have demonstrated state-of-the-art performance in cases where the forward operator is known (i.e. non-blind). However, the applicability of the method to blind inverse problems has yet to be explored. In this work, we show that we can indeed solve a family of blind inverse problems by constructing another diffusion prior for the forward operator. Specifically, parallel reverse diffusion guided by gradients from the intermediate stages enables joint optimization of both the forward operator parameters as well as the image, such that both are jointly estimated at the end of the parallel reverse diffusion procedure. We show the efficacy of our method on two representative tasks -- blind deblurring, and imaging through turbulence -- and show that our method yields state-of-the-art performance, while also being flexible to be applicable to general blind inverse problems when we know the functional forms.

Embedding inversion, i.e., reconstructing text given its embedding and black-box access to the embedding encoder, is a fundamental problem in both NLP and security. From the NLP perspective, it helps determine how much semantic information about the input is retained in the embedding. From the security perspective, it measures how much information is leaked by vector databases and embedding-based retrieval systems. State-of-the-art methods for embedding inversion, such as vec2text, have high accuracy but require (a) training a separate model for each embedding, and (b) a large number of queries to the corresponding encoder. We design, implement, and evaluate ZSInvert, a zero-shot inversion method based on the recently proposed adversarial decoding technique. ZSInvert is fast, query-efficient, and can be used for any text embedding without training an embedding-specific inversion model. We measure the effectiveness of ZSInvert on several embeddings and demonstrate that it recovers key semantic information about the corresponding texts.

By comparing the original and target prompts in editing task, we can obtain numerous editing pairs, each comprising an object and its corresponding editing target. To allow editability while maintaining fidelity to the input image, existing editing methods typically involve a fixed number of inversion steps that project the whole input image to its noisier latent representation, followed by a denoising process guided by the target prompt. However, we find that the optimal number of inversion steps for achieving ideal editing results varies significantly among different editing pairs, owing to varying editing difficulties. Therefore, the current literature, which relies on a fixed number of inversion steps, produces sub-optimal generation quality, especially when handling multiple editing pairs in a natural image. To this end, we propose a new image editing paradigm, dubbed Object-aware Inversion and Reassembly (OIR), to enable object-level fine-grained editing. Specifically, we design a new search metric, which determines the optimal inversion steps for each editing pair, by jointly considering the editability of the target and the fidelity of the non-editing region. We use our search metric to find the optimal inversion step for each editing pair when editing an image. We then edit these editing pairs separately to avoid concept mismatch. Subsequently, we propose an additional reassembly step to seamlessly integrate the respective editing results and the non-editing region to obtain the final edited image. To systematically evaluate the effectiveness of our method, we collect two datasets for benchmarking single- and multi-object editing, respectively. Experiments demonstrate that our method achieves superior performance in editing object shapes, colors, materials, categories, etc., especially in multi-object editing scenarios.

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each task. Most inverse tasks can be formulated as inferring a posterior distribution over data (e.g., a full image) given a measurement (e.g., a masked image). This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. To cope with this challenge, we propose a variational approach that by design seeks to approximate the true posterior distribution. We show that our approach naturally leads to regularization by denoising diffusion process (RED-Diff) where denoisers at different timesteps concurrently impose different structural constraints over the image. To gauge the contribution of denoisers from different timesteps, we propose a weighting mechanism based on signal-to-noise-ratio (SNR). Our approach provides a new variational perspective for solving inverse problems with diffusion models, allowing us to formulate sampling as stochastic optimization, where one can simply apply off-the-shelf solvers with lightweight iterates. Our experiments for image restoration tasks such as inpainting and superresolution demonstrate the strengths of our method compared with state-of-the-art sampling-based diffusion models.

Text-to-image diffusion models offer powerful image editing capabilities. To edit real images, many methods rely on the inversion of the image into Gaussian noise. A common approach to invert an image is to gradually add noise to the image, where the noise is determined by reversing the sampling equation. This process has an inherent tradeoff between reconstruction and editability, limiting the editing of challenging images such as highly-detailed ones. Recognizing the reliance of text-to-image models inversion on a text condition, this work explores the importance of the condition choice. We show that a condition that precisely aligns with the input image significantly improves the inversion quality. Based on our findings, we introduce Tight Inversion, an inversion method that utilizes the most possible precise condition -- the input image itself. This tight condition narrows the distribution of the model's output and enhances both reconstruction and editability. We demonstrate the effectiveness of our approach when combined with existing inversion methods through extensive experiments, evaluating the reconstruction accuracy as well as the integration with various editing methods.

Diffusion models have achieved remarkable success in the domain of text-guided image generation and, more recently, in text-guided image editing. A commonly adopted strategy for editing real images involves inverting the diffusion process to obtain a noisy representation of the original image, which is then denoised to achieve the desired edits. However, current methods for diffusion inversion often struggle to produce edits that are both faithful to the specified text prompt and closely resemble the source image. To overcome these limitations, we introduce a novel and adaptable diffusion inversion technique for real image editing, which is grounded in a theoretical analysis of the role of eta in the DDIM sampling equation for enhanced editability. By designing a universal diffusion inversion method with a time- and region-dependent eta function, we enable flexible control over the editing extent. Through a comprehensive series of quantitative and qualitative assessments, involving a comparison with a broad array of recent methods, we demonstrate the superiority of our approach. Our method not only sets a new benchmark in the field but also significantly outperforms existing strategies.

Machine unlearning seeks to remove the influence of particular data or class from trained models to meet privacy, legal, or ethical requirements. Existing unlearning methods tend to forget shallowly: phenomenon of an unlearned model pretend to forget by adjusting only the model response, while its internal representations retain information sufficiently to restore the forgotten data or behavior. We empirically confirm the widespread shallowness by reverting the forgetting effect of various unlearning methods via training-free performance recovery attack and gradient-inversion-based data reconstruction attack. To address this vulnerability fundamentally, we define a theoretical criterion of ``deep forgetting'' based on one-point-contraction of feature representations of data to forget. We also propose an efficient approximation algorithm, and use it to construct a novel general-purpose unlearning algorithm: One-Point-Contraction (OPC). Empirical evaluations on image classification unlearning benchmarks show that OPC achieves not only effective unlearning performance but also superior resilience against both performance recovery attack and gradient-inversion attack. The distinctive unlearning performance of OPC arises from the deep feature forgetting enforced by its theoretical foundation, and recaps the need for improved robustness of machine unlearning methods.

The current GAN inversion methods typically can only edit the appearance and shape of a single object and background while overlooking spatial information. In this work, we propose a 3D editing framework, 3D-GOI, to enable multifaceted editing of affine information (scale, translation, and rotation) on multiple objects. 3D-GOI realizes the complex editing function by inverting the abundance of attribute codes (object shape/appearance/scale/rotation/translation, background shape/appearance, and camera pose) controlled by GIRAFFE, a renowned 3D GAN. Accurately inverting all the codes is challenging, 3D-GOI solves this challenge following three main steps. First, we segment the objects and the background in a multi-object image. Second, we use a custom Neural Inversion Encoder to obtain coarse codes of each object. Finally, we use a round-robin optimization algorithm to get precise codes to reconstruct the image. To the best of our knowledge, 3D-GOI is the first framework to enable multifaceted editing on multiple objects. Both qualitative and quantitative experiments demonstrate that 3D-GOI holds immense potential for flexible, multifaceted editing in complex multi-object scenes.Our project and code are released at https://3d-goi.github.io .

Deep generative models based on neural differential equations have quickly become the state-of-the-art for numerous generation tasks across many different applications. These models rely on ODE/SDE solvers which integrate from a prior distribution to the data distribution. In many applications it is highly desirable to then integrate in the other direction. The standard solvers, however, accumulate discretization errors which don't align with the forward trajectory, thereby prohibiting an exact inversion. In applications where the precision of the generative model is paramount this inaccuracy in inversion is often unacceptable. Current approaches to solving the inversion of these models results in significant downstream issues with poor stability and low-order of convergence; moreover, they are strictly limited to the ODE domain. In this work, we propose a new family of reversible exponential (stochastic) Runge-Kutta solvers which we refer to as Rex developed by an application of Lawson methods to convert any explicit (stochastic) Runge-Kutta scheme into a reversible one. In addition to a rigorous theoretical analysis of the proposed solvers, we also empirically demonstrate the utility of Rex on improving the sampling of Boltzmann distributions with flow models, and improving image generation and editing capabilities with diffusion models.

In image editing employing diffusion models, it is crucial to preserve the reconstruction quality of the original image while changing its style. Although existing methods ensure reconstruction quality through optimization, a drawback of these is the significant amount of time required for optimization. In this paper, we propose negative-prompt inversion, a method capable of achieving equivalent reconstruction solely through forward propagation without optimization, thereby enabling much faster editing processes. We experimentally demonstrate that the reconstruction quality of our method is comparable to that of existing methods, allowing for inversion at a resolution of 512 pixels and with 50 sampling steps within approximately 5 seconds, which is more than 30 times faster than null-text inversion. Reduction of the computation time by the proposed method further allows us to use a larger number of sampling steps in diffusion models to improve the reconstruction quality with a moderate increase in computation time.

Given the ubiquity of deep neural networks, it is important that these models do not reveal information about sensitive data that they have been trained on. In model inversion attacks, a malicious user attempts to recover the private dataset used to train a supervised neural network. A successful model inversion attack should generate realistic and diverse samples that accurately describe each of the classes in the private dataset. In this work, we provide a probabilistic interpretation of model inversion attacks, and formulate a variational objective that accounts for both diversity and accuracy. In order to optimize this variational objective, we choose a variational family defined in the code space of a deep generative model, trained on a public auxiliary dataset that shares some structural similarity with the target dataset. Empirically, our method substantially improves performance in terms of target attack accuracy, sample realism, and diversity on datasets of faces and chest X-ray images.

We present One4D, a unified framework for 4D generation and reconstruction that produces dynamic 4D content as synchronized RGB frames and pointmaps. By consistently handling varying sparsities of conditioning frames through a Unified Masked Conditioning (UMC) mechanism, One4D can seamlessly transition between 4D generation from a single image, 4D reconstruction from a full video, and mixed generation and reconstruction from sparse frames. Our framework adapts a powerful video generation model for joint RGB and pointmap generation, with carefully designed network architectures. The commonly used diffusion finetuning strategies for depthmap or pointmap reconstruction often fail on joint RGB and pointmap generation, quickly degrading the base video model. To address this challenge, we introduce Decoupled LoRA Control (DLC), which employs two modality-specific LoRA adapters to form decoupled computation branches for RGB frames and pointmaps, connected by lightweight, zero-initialized control links that gradually learn mutual pixel-level consistency. Trained on a mixture of synthetic and real 4D datasets under modest computational budgets, One4D produces high-quality RGB frames and accurate pointmaps across both generation and reconstruction tasks. This work represents a step toward general, high-quality geometry-based 4D world modeling using video diffusion models. Project page: https://mizhenxing.github.io/One4D

Given the existence of various forward and inverse problems in combustion studies and applications that necessitate distinct methods for resolution, a framework to solve them in a unified way is critically needed. A promising approach is the integration of machine learning methods with governing equations of combustion systems, which exhibits superior generality and few-shot learning ability compared to purely data-driven methods. In this work, the FlamePINN-1D framework is proposed to solve the forward and inverse problems of 1D laminar flames based on physics-informed neural networks. Three cases with increasing complexity have been tested: Case 1 are freely-propagating premixed (FPP) flames with simplified physical models, while Case 2 and Case 3 are FPP and counterflow premixed (CFP) flames with detailed models, respectively. For forward problems, FlamePINN-1D aims to solve the flame fields and infer the unknown eigenvalues (such as laminar flame speeds) under the constraints of governing equations and boundary conditions. For inverse problems, FlamePINN-1D aims to reconstruct the continuous fields and infer the unknown parameters (such as transport and chemical kinetics parameters) from noisy sparse observations of the flame. Our results strongly validate these capabilities of FlamePINN-1D across various flames and working conditions. Compared to traditional methods, FlamePINN-1D is differentiable and mesh-free, exhibits no discretization errors, and is easier to implement for inverse problems. The inverse problem results also indicate the possibility of optimizing chemical mechanisms from measurements of laboratory 1D flames. Furthermore, some proposed strategies, such as hard constraints and thin-layer normalization, are proven to be essential for the robust learning of FlamePINN-1D. The code for this paper is partially available at https://github.com/CAME-THU/FlamePINN-1D.

Despite unconditional feature inversion being the foundation of many image synthesis applications, training an inverter demands a high computational budget, large decoding capacity and imposing conditions such as autoregressive priors. To address these limitations, we propose the use of adversarially robust representations as a perceptual primitive for feature inversion. We train an adversarially robust encoder to extract disentangled and perceptually-aligned image representations, making them easily invertible. By training a simple generator with the mirror architecture of the encoder, we achieve superior reconstruction quality and generalization over standard models. Based on this, we propose an adversarially robust autoencoder and demonstrate its improved performance on style transfer, image denoising and anomaly detection tasks. Compared to recent ImageNet feature inversion methods, our model attains improved performance with significantly less complexity.

3D GAN inversion aims to achieve high reconstruction fidelity and reasonable 3D geometry simultaneously from a single image input. However, existing 3D GAN inversion methods rely on time-consuming optimization for each individual case. In this work, we introduce a novel encoder-based inversion framework based on EG3D, one of the most widely-used 3D GAN models. We leverage the inherent properties of EG3D's latent space to design a discriminator and a background depth regularization. This enables us to train a geometry-aware encoder capable of converting the input image into corresponding latent code. Additionally, we explore the feature space of EG3D and develop an adaptive refinement stage that improves the representation ability of features in EG3D to enhance the recovery of fine-grained textural details. Finally, we propose an occlusion-aware fusion operation to prevent distortion in unobserved regions. Our method achieves impressive results comparable to optimization-based methods while operating up to 500 times faster. Our framework is well-suited for applications such as semantic editing.

The multi-step denoising process in diffusion and Flow Matching models causes major efficiency issues, which motivates research on few-step generation. We present Solution Flow Models (SoFlow), a framework for one-step generation from scratch. By analyzing the relationship between the velocity function and the solution function of the velocity ordinary differential equation (ODE), we propose a Flow Matching loss and a solution consistency loss to train our models. The Flow Matching loss allows our models to provide estimated velocity fields for Classifier-Free Guidance (CFG) during training, which improves generation performance. Notably, our consistency loss does not require the calculation of the Jacobian-vector product (JVP), a common requirement in recent works that is not well-optimized in deep learning frameworks like PyTorch. Experimental results indicate that, when trained from scratch using the same Diffusion Transformer (DiT) architecture and an equal number of training epochs, our models achieve better FID-50K scores than MeanFlow models on the ImageNet 256x256 dataset.

Recent advancements in diffusion models (DMs) have been propelled by alignment methods that post-train models to better conform to human preferences. However, these approaches typically require computation-intensive training of a base model and a reward model, which not only incurs substantial computational overhead but may also compromise model accuracy and training efficiency. To address these limitations, we propose Inversion-DPO, a novel alignment framework that circumvents reward modeling by reformulating Direct Preference Optimization (DPO) with DDIM inversion for DMs. Our method conducts intractable posterior sampling in Diffusion-DPO with the deterministic inversion from winning and losing samples to noise and thus derive a new post-training paradigm. This paradigm eliminates the need for auxiliary reward models or inaccurate appromixation, significantly enhancing both precision and efficiency of training. We apply Inversion-DPO to a basic task of text-to-image generation and a challenging task of compositional image generation. Extensive experiments show substantial performance improvements achieved by Inversion-DPO compared to existing post-training methods and highlight the ability of the trained generative models to generate high-fidelity compositionally coherent images. For the post-training of compostitional image geneation, we curate a paired dataset consisting of 11,140 images with complex structural annotations and comprehensive scores, designed to enhance the compositional capabilities of generative models. Inversion-DPO explores a new avenue for efficient, high-precision alignment in diffusion models, advancing their applicability to complex realistic generation tasks. Our code is available at https://github.com/MIGHTYEZ/Inversion-DPO

The use of deep unfolding networks in compressive sensing (CS) has seen wide success as they provide both simplicity and interpretability. However, since most deep unfolding networks are iterative, this incurs significant redundancies in the network. In this work, we propose a novel recursion-based framework to enhance the efficiency of deep unfolding models. First, recursions are used to effectively eliminate the redundancies in deep unfolding networks. Secondly, we randomize the number of recursions during training to decrease the overall training time. Finally, to effectively utilize the power of recursions, we introduce a learnable unit to modulate the features of the model based on both the total number of iterations and the current iteration index. To evaluate the proposed framework, we apply it to both ISTA-Net+ and COAST. Extensive testing shows that our proposed framework allows the network to cut down as much as 75% of its learnable parameters while mostly maintaining its performance, and at the same time, it cuts around 21% and 42% from the training time for ISTA-Net+ and COAST respectively. Moreover, when presented with a limited training dataset, the recursive models match or even outperform their respective non-recursive baseline. Codes and pretrained models are available at https://github.com/Rawwad-Alhejaili/Recursions-Are-All-You-Need .

Many machine learning methods operate by inverting a neural network at inference time, which has become a popular technique for solving inverse problems in computer vision, robotics, and graphics. However, these methods often involve gradient descent through a highly non-convex loss landscape, causing the optimization process to be unstable and slow. We introduce a method that learns a loss landscape where gradient descent is efficient, bringing massive improvement and acceleration to the inversion process. We demonstrate this advantage on a number of methods for both generative and discriminative tasks, including GAN inversion, adversarial defense, and 3D human pose reconstruction.

While backpropagation (BP) is the mainstream approach for gradient computation in neural network training, its heavy reliance on the chain rule of differentiation constrains the designing flexibility of network architecture and training pipelines. We avoid the recursive computation in BP and develop a unified likelihood ratio (ULR) method for gradient estimation with just one forward propagation. Not only can ULR be extended to train a wide variety of neural network architectures, but the computation flow in BP can also be rearranged by ULR for better device adaptation. Moreover, we propose several variance reduction techniques to further accelerate the training process. Our experiments offer numerical results across diverse aspects, including various neural network training scenarios, computation flow rearrangement, and fine-tuning of pre-trained models. All findings demonstrate that ULR effectively enhances the flexibility of neural network training by permitting localized module training without compromising the global objective and significantly boosts the network robustness.

Effective image inversion in rectified flow models - mapping real images to editable latent representations - is crucial for practical image editing applications; however, achieving optimal balance between reconstruction fidelity and editing flexibility remains a fundamental challenge. In this work, we introduce the Optimal Transport Inversion Pipeline (OTIP), a zero-shot framework that leverages optimal transport theory to guide the inversion process in rectified flow models. Our underlying hypothesis is that incorporating transport-based guidance during the reverse diffusion process can effectively balance reconstruction accuracy and editing controllability through principled trajectory optimization. The method computes optimal transport paths between image and noise distributions while maintaining computational efficiency. Our approach achieves high-fidelity reconstruction with LPIPS scores of 0.001 and SSIM of 0.992 on face editing benchmarks, demonstrating superior preservation of fine-grained details compared to existing methods. We evaluate the framework across multiple editing tasks, observing 7.8% to 12.9% improvements in reconstruction loss over RF-Inversion on the LSUN-Bedroom and LSUN-Church datasets, respectively. For semantic face editing, our method achieves an 11.2% improvement in identity preservation and a 1.6% enhancement in perceptual quality, while maintaining computational efficiency comparable to baseline approaches. Qualitatively, our method produces visually compelling edits with superior semantic consistency and fine-grained detail preservation across diverse editing scenarios. Code is available at: https://github.com/marianlupascu/OT-Inversion

We present adversarial flow models, a class of generative models that unifies adversarial models and flow models. Our method supports native one-step or multi-step generation and is trained using the adversarial objective. Unlike traditional GANs, where the generator learns an arbitrary transport plan between the noise and the data distributions, our generator learns a deterministic noise-to-data mapping, which is the same optimal transport as in flow-matching models. This significantly stabilizes adversarial training. Also, unlike consistency-based methods, our model directly learns one-step or few-step generation without needing to learn the intermediate timesteps of the probability flow for propagation. This saves model capacity, reduces training iterations, and avoids error accumulation. Under the same 1NFE setting on ImageNet-256px, our B/2 model approaches the performance of consistency-based XL/2 models, while our XL/2 model creates a new best FID of 2.38. We additionally show the possibility of end-to-end training of 56-layer and 112-layer models through depth repetition without any intermediate supervision, and achieve FIDs of 2.08 and 1.94 using a single forward pass, surpassing their 2NFE and 4NFE counterparts.

Ever since the original algorithm by Nesterov (1983), the true nature of the acceleration phenomenon has remained elusive, with various interpretations of why the method is actually faster. The diagnosis of the algorithm through the lens of Ordinary Differential Equations (ODEs) and the corresponding dynamical system formulation to explain the underlying dynamics has a rich history. In the literature, the ODEs that explain algorithms are typically derived by considering the limiting case of the algorithm maps themselves, that is, an ODE formulation follows the development of an algorithm. This obfuscates the underlying higher order principles and thus provides little evidence of the working of the algorithm. Such has been the case with Nesterov algorithm and the various analogies used to describe the acceleration phenomena, viz, momentum associated with the rolling of a Heavy-Ball down a slope, Hessian damping etc. The main focus of our work is to ideate the genesis of the Nesterov algorithm from the viewpoint of dynamical systems leading to demystifying the mathematical rigour behind the algorithm. Instead of reverse engineering ODEs from discrete algorithms, this work explores tools from the recently developed control paradigm titled Passivity and Immersion approach and the Geometric Singular Perturbation theory which are applied to arrive at the formulation of a dynamical system that explains and models the acceleration phenomena. This perspective helps to gain insights into the various terms present and the sequence of steps used in Nesterovs accelerated algorithm for the smooth strongly convex and the convex case. The framework can also be extended to derive the acceleration achieved using the triple momentum method and provides justifications for the non-convergence to the optimal solution in the Heavy-Ball method.

Recent advances in diffusion and flow-based generative models have demonstrated remarkable success in image restoration tasks, achieving superior perceptual quality compared to traditional deep learning approaches. However, these methods either require numerous sampling steps to generate high-quality images, resulting in significant computational overhead, or rely on model distillation, which usually imposes a fixed fidelity-realism trade-off and thus lacks flexibility. In this paper, we introduce OFTSR, a novel flow-based framework for one-step image super-resolution that can produce outputs with tunable levels of fidelity and realism. Our approach first trains a conditional flow-based super-resolution model to serve as a teacher model. We then distill this teacher model by applying a specialized constraint. Specifically, we force the predictions from our one-step student model for same input to lie on the same sampling ODE trajectory of the teacher model. This alignment ensures that the student model's single-step predictions from initial states match the teacher's predictions from a closer intermediate state. Through extensive experiments on challenging datasets including FFHQ (256times256), DIV2K, and ImageNet (256times256), we demonstrate that OFTSR achieves state-of-the-art performance for one-step image super-resolution, while having the ability to flexibly tune the fidelity-realism trade-off. Code and pre-trained models are available at https://github.com/yuanzhi-zhu/OFTSR and https://huggingface.co/Yuanzhi/OFTSR, respectively.

Diffusion models (DMs) excel in photorealism, image editing, and solving inverse problems, aided by classifier-free guidance and image inversion techniques. However, rectified flow models (RFMs) remain underexplored for these tasks. Existing DM-based methods often require additional training, lack generalization to pretrained latent models, underperform, and demand significant computational resources due to extensive backpropagation through ODE solvers and inversion processes. In this work, we first develop a theoretical and empirical understanding of the vector field dynamics of RFMs in efficiently guiding the denoising trajectory. Our findings reveal that we can navigate the vector field in a deterministic and gradient-free manner. Utilizing this property, we propose FlowChef, which leverages the vector field to steer the denoising trajectory for controlled image generation tasks, facilitated by gradient skipping. FlowChef is a unified framework for controlled image generation that, for the first time, simultaneously addresses classifier guidance, linear inverse problems, and image editing without the need for extra training, inversion, or intensive backpropagation. Finally, we perform extensive evaluations and show that FlowChef significantly outperforms baselines in terms of performance, memory, and time requirements, achieving new state-of-the-art results. Project Page: https://flowchef.github.io.

Text-guided diffusion models have become a popular tool in image synthesis, known for producing high-quality and diverse images. However, their application to editing real images often encounters hurdles primarily due to the text condition deteriorating the reconstruction quality and subsequently affecting editing fidelity. Null-text Inversion (NTI) has made strides in this area, but it fails to capture spatial context and requires computationally intensive per-timestep optimization. Addressing these challenges, we present Noise Map Guidance (NMG), an inversion method rich in a spatial context, tailored for real-image editing. Significantly, NMG achieves this without necessitating optimization, yet preserves the editing quality. Our empirical investigations highlight NMG's adaptability across various editing techniques and its robustness to variants of DDIM inversions.

This paper investigates the utility gain of using Iterative Bayesian Update (IBU) for private discrete distribution estimation using data obfuscated with Locally Differentially Private (LDP) mechanisms. We compare the performance of IBU to Matrix Inversion (MI), a standard estimation technique, for seven LDP mechanisms designed for one-time data collection and for other seven LDP mechanisms designed for multiple data collections (e.g., RAPPOR). To broaden the scope of our study, we also varied the utility metric, the number of users n, the domain size k, and the privacy parameter ε, using both synthetic and real-world data. Our results suggest that IBU can be a useful post-processing tool for improving the utility of LDP mechanisms in different scenarios without any additional privacy cost. For instance, our experiments show that IBU can provide better utility than MI, especially in high privacy regimes (i.e., when ε is small). Our paper provides insights for practitioners to use IBU in conjunction with existing LDP mechanisms for more accurate and privacy-preserving data analysis. Finally, we implemented IBU for all fourteen LDP mechanisms into the state-of-the-art multi-freq-ldpy Python package (https://pypi.org/project/multi-freq-ldpy/) and open-sourced all our code used for the experiments as tutorials.

The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differential categories for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.

Inverse of an invertible convolution is an important operation that comes up in Normalizing Flows, Image Deblurring, etc. The naive algorithm for backpropagation of this operation using Gaussian elimination has running time O(n^3) where n is the number of pixels in the image. We give a fast parallel backpropagation algorithm with running time O(n) for a square image and provide a GPU implementation of the same. Inverse Convolutions are usually used in Normalizing Flows in the sampling pass, making them slow. We propose to use Inverse Convolutions in the forward (image to latent vector) pass of the Normalizing flow. Since the sampling pass is the inverse of the forward pass, it will use convolutions only, resulting in efficient sampling times. We use our parallel backpropagation algorithm for optimizing the inverse convolution layer resulting in fast training times also. We implement this approach in various Normalizing Flow backbones, resulting in our Inverse-Flow models. We benchmark Inverse-Flow on standard datasets and show significantly improved sampling times with similar bits per dimension compared to previous models.

Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are fine-tuned for the application at hand. Although this tuning process can require large computational costs, recent work has shown that these costs can be reduced by line search methods that iteratively adjust the stepsize. We propose an alternative approach to stochastic line search by using a new algorithm based on forward step model building. This model building step incorporates second-order information that allows adjusting not only the stepsize but also the search direction. Noting that deep learning model parameters come in groups (layers of tensors), our method builds its model and calculates a new step for each parameter group. This novel diagonalization approach makes the selected step lengths adaptive. We provide convergence rate analysis, and experimentally show that the proposed algorithm achieves faster convergence and better generalization in well-known test problems. More precisely, SMB requires less tuning, and shows comparable performance to other adaptive methods.

This paper introduces UnDiff, a diffusion probabilistic model capable of solving various speech inverse tasks. Being once trained for speech waveform generation in an unconditional manner, it can be adapted to different tasks including degradation inversion, neural vocoding, and source separation. In this paper, we, first, tackle the challenging problem of unconditional waveform generation by comparing different neural architectures and preconditioning domains. After that, we demonstrate how the trained unconditional diffusion could be adapted to different tasks of speech processing by the means of recent developments in post-training conditioning of diffusion models. Finally, we demonstrate the performance of the proposed technique on the tasks of bandwidth extension, declipping, vocoding, and speech source separation and compare it to the baselines. The codes are publicly available.

Recent progress in text-to-image (T2I) models enables high-quality image generation with flexible textual control. To utilize the abundant visual priors in the off-the-shelf T2I models, a series of methods try to invert an image to proper embedding that aligns with the semantic space of the T2I model. However, these image-to-text (I2T) inversion methods typically need multiple source images containing the same concept or struggle with the imbalance between editing flexibility and visual fidelity. In this work, we point out that the critical problem lies in the foreground-background entanglement when learning an intended concept, and propose a simple and effective baseline for single-image I2T inversion, named SingleInsert. SingleInsert adopts a two-stage scheme. In the first stage, we regulate the learned embedding to concentrate on the foreground area without being associated with the irrelevant background. In the second stage, we finetune the T2I model for better visual resemblance and devise a semantic loss to prevent the language drift problem. With the proposed techniques, SingleInsert excels in single concept generation with high visual fidelity while allowing flexible editing. Additionally, SingleInsert can perform single-image novel view synthesis and multiple concepts composition without requiring joint training. To facilitate evaluation, we design an editing prompt list and introduce a metric named Editing Success Rate (ESR) for quantitative assessment of editing flexibility. Our project page is: https://jarrentwu1031.github.io/SingleInsert-web/

Recent diffusion-based models achieve photorealism in image inpainting but require many sampling steps, limiting practical use. Few-step text-to-image models offer faster generation, but naively applying them to inpainting yields poor harmonization and artifacts between the background and inpainted region. We trace this cause to random Gaussian noise initialization, which under low function evaluations causes semantic misalignment and reduced fidelity. To overcome this, we propose InverFill, a one-step inversion method tailored for inpainting that injects semantic information from the input masked image into the initial noise, enabling high-fidelity few-step inpainting. Instead of training inpainting models, InverFill leverages few-step text-to-image models in a blended sampling pipeline with semantically aligned noise as input, significantly improving vanilla blended sampling and even matching specialized inpainting models at low NFEs. Moreover, InverFill does not require real-image supervision and only adds minimal inference overhead. Extensive experiments show that InverFill consistently boosts baseline few-step models, improving image quality and text coherence without costly retraining or heavy iterative optimization.

Text-driven diffusion models have significantly advanced the image editing performance by using text prompts as inputs. One crucial step in text-driven image editing is to invert the original image into a latent noise code conditioned on the source prompt. While previous methods have achieved promising results by refactoring the image synthesizing process, the inverted latent noise code is tightly coupled with the source prompt, limiting the image editability by target text prompts. To address this issue, we propose a novel method called Source Prompt Disentangled Inversion (SPDInv), which aims at reducing the impact of source prompt, thereby enhancing the text-driven image editing performance by employing diffusion models. To make the inverted noise code be independent of the given source prompt as much as possible, we indicate that the iterative inversion process should satisfy a fixed-point constraint. Consequently, we transform the inversion problem into a searching problem to find the fixed-point solution, and utilize the pre-trained diffusion models to facilitate the searching process. The experimental results show that our proposed SPDInv method can effectively mitigate the conflicts between the target editing prompt and the source prompt, leading to a significant decrease in editing artifacts. In addition to text-driven image editing, with SPDInv we can easily adapt customized image generation models to localized editing tasks and produce promising performance. The source code are available at https://github.com/leeruibin/SPDInv.

The generative power of diffusion models (DMs) has recently enabled high-performing decision-making algorithms in offline reinforcement learning (RL), achieving state-of-the-art results across standard benchmarks. Among them, Diffusion Q-Learning (DQL) stands out as a leading method for its consistently strong performance. Nevertheless, DQL remains limited in practice due to its reliance on multi-step denoising for action generation during both training and inference. Although one-step denoising is desirable, simply applying it to DQL leads to a drastic performance drop. In this work, we revisit DQL and identify its core limitations. We then propose One-Step Flow Q-Learning (OFQL), a novel framework that enables efficient one-step action generation during both training and inference, without requiring auxiliary models, distillation, or multi-phase training. Specifically, OFQL reformulates DQL within the sample-efficient Flow Matching (FM) framework. While conventional FM induces curved generative trajectories that impede one-step generation, OFQL instead learns an average velocity field that facilitates direct, accurate action generation. Collectively, OFQL eliminates the need for multi-step sampling and recursive gradient updates in DQL, resulting in faster and more robust training and inference. Extensive experiments on the D4RL benchmark demonstrate that OFQL outperforms DQL and other diffusion-based baselines, while substantially reducing both training and inference time compared to DQL.

Diffusion models have emerged as a formidable tool for training-free conditional generation.However, a key hurdle in inference-time guidance techniques is the need for compute-heavy backpropagation through the diffusion network for estimating the guidance direction. Moreover, these techniques often require handcrafted parameter tuning on a case-by-case basis. Although some recent works have introduced minimal compute methods for linear inverse problems, a generic lightweight guidance solution to both linear and non-linear guidance problems is still missing. To this end, we propose Dreamguider, a method that enables inference-time guidance without compute-heavy backpropagation through the diffusion network. The key idea is to regulate the gradient flow through a time-varying factor. Moreover, we propose an empirical guidance scale that works for a wide variety of tasks, hence removing the need for handcrafted parameter tuning. We further introduce an effective lightweight augmentation strategy that significantly boosts the performance during inference-time guidance. We present experiments using Dreamguider on multiple tasks across multiple datasets and models to show the effectiveness of the proposed modules. To facilitate further research, we will make the code public after the review process.

We give explicit low-rank bilinear non-commutative schemes for multiplying structured n times n matrices with 2 leq n leq 5, which serve as building blocks for recursive algorithms with improved multiplicative factors in asymptotic complexity. Our schemes are discovered over F_2 or F_3 and lifted to Z or Q. Using a flip graph search over tensor decompositions, we derive schemes for general, upper-triangular, lower-triangular, symmetric, and skew-symmetric inputs, as well as products of a structured matrix with its transpose. In particular, we obtain 4 times 4 rank-34 schemes: (i) multiplying a general matrix by its transpose using 10 recursive calls, improving the factor from 26/41 (0.634) to 8/13 (0.615); and (ii) multiplying an upper-triangular matrix by a general matrix using 12 recursive calls, improving the factor from 8/13 (0.615) to 22/37 (0.595). Additionally, using F_3 flip graphs, we discover schemes over Q that fundamentally require the inverse of 2, including a 2 times 2 symmetric-symmetric multiplication of rank 5 and a 3 times 3 skew-symmetric-general multiplication of rank 14 (improving upon AlphaTensor's 15).

Whenever we use devices to take measurements, calibration is indispensable. While the purpose of calibration is to reduce bias and uncertainty in the measurements, it can be quite difficult, expensive, and sometimes even impossible to implement. We study a challenging problem called self-calibration, i.e., the task of designing an algorithm for devices so that the algorithm is able to perform calibration automatically. More precisely, we consider the setup y = A(d) x + epsilon where only partial information about the sensing matrix A(d) is known and where A(d) linearly depends on d. The goal is to estimate the calibration parameter d (resolve the uncertainty in the sensing process) and the signal/object of interests x simultaneously. For three different models of practical relevance, we show how such a bilinear inverse problem, including blind deconvolution as an important example, can be solved via a simple linear least squares approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus potentially allowing for real-time deployment. We also present a variation of the least squares approach, which leads to a~spectral method, where the solution to the bilinear inverse problem can be found by computing the singular vector associated with the smallest singular value of a certain matrix derived from the bilinear system. Explicit theoretical guarantees and stability theory are derived for both techniques; and the number of sampling complexity is nearly optimal (up to a poly-log factor). Applications in imaging sciences and signal processing are discussed and numerical simulations are presented to demonstrate the effectiveness and efficiency of our approach.

While generative artificial intelligence has advanced significantly across text, image, audio, and video domains, 3D generation remains comparatively underdeveloped due to fundamental challenges such as data scarcity, algorithmic limitations, and ecosystem fragmentation. To this end, we present Step1X-3D, an open framework addressing these challenges through: (1) a rigorous data curation pipeline processing >5M assets to create a 2M high-quality dataset with standardized geometric and textural properties; (2) a two-stage 3D-native architecture combining a hybrid VAE-DiT geometry generator with an diffusion-based texture synthesis module; and (3) the full open-source release of models, training code, and adaptation modules. For geometry generation, the hybrid VAE-DiT component produces TSDF representations by employing perceiver-based latent encoding with sharp edge sampling for detail preservation. The diffusion-based texture synthesis module then ensures cross-view consistency through geometric conditioning and latent-space synchronization. Benchmark results demonstrate state-of-the-art performance that exceeds existing open-source methods, while also achieving competitive quality with proprietary solutions. Notably, the framework uniquely bridges the 2D and 3D generation paradigms by supporting direct transfer of 2D control techniques~(e.g., LoRA) to 3D synthesis. By simultaneously advancing data quality, algorithmic fidelity, and reproducibility, Step1X-3D aims to establish new standards for open research in controllable 3D asset generation.

In this paper we provide a new method to certify that a nearby polynomial system has a singular isolated root with a prescribed multiplicity structure. More precisely, given a polynomial system f =(f_1, ldots, f_N)in C[x_1, ldots, x_n]^N, we present a Newton iteration on an extended deflated system that locally converges, under regularity conditions, to a small deformation of f such that this deformed system has an exact singular root. The iteration simultaneously converges to the coordinates of the singular root and the coefficients of the so called inverse system that describes the multiplicity structure at the root. We use $alpha$-theory test to certify the quadratic convergence, and togive bounds on the size of the deformation and on the approximation error. The approach relies on an analysis of the punctual Hilbert scheme, for which we provide a new description. We show in particular that some of its strata can be rationally parametrized and exploit these parametrizations in the certification. We show in numerical experimentation how the approximate inverse system can be computed as a starting point of the Newton iterations and the fast numerical convergence to the singular root with its multiplicity structure, certified by our criteria.

Diffusion-based voice conversion (VC) techniques such as VoiceGrad have attracted interest because of their high VC performance in terms of speech quality and speaker similarity. However, a notable limitation is the slow inference caused by the multi-step reverse diffusion. Therefore, we propose FastVoiceGrad, a novel one-step diffusion-based VC that reduces the number of iterations from dozens to one while inheriting the high VC performance of the multi-step diffusion-based VC. We obtain the model using adversarial conditional diffusion distillation (ACDD), leveraging the ability of generative adversarial networks and diffusion models while reconsidering the initial states in sampling. Evaluations of one-shot any-to-any VC demonstrate that FastVoiceGrad achieves VC performance superior to or comparable to that of previous multi-step diffusion-based VC while enhancing the inference speed. Audio samples are available at https://www.kecl.ntt.co.jp/people/kaneko.takuhiro/projects/fastvoicegrad/.

Generative models like Flow Matching have achieved state-of-the-art performance but are often hindered by a computationally expensive iterative sampling process. To address this, recent work has focused on few-step or one-step generation by learning the average velocity field, which directly maps noise to data. MeanFlow, a leading method in this area, learns this field by enforcing a differential identity that connects the average and instantaneous velocities. In this work, we argue that this differential formulation is a limiting special case of a more fundamental principle. We return to the first principles of average velocity and leverage the additivity property of definite integrals. This leads us to derive a novel, purely algebraic identity we term Interval Splitting Consistency. This identity establishes a self-referential relationship for the average velocity field across different time intervals without resorting to any differential operators. Based on this principle, we introduce SplitMeanFlow, a new training framework that enforces this algebraic consistency directly as a learning objective. We formally prove that the differential identity at the core of MeanFlow is recovered by taking the limit of our algebraic consistency as the interval split becomes infinitesimal. This establishes SplitMeanFlow as a direct and more general foundation for learning average velocity fields. From a practical standpoint, our algebraic approach is significantly more efficient, as it eliminates the need for JVP computations, resulting in simpler implementation, more stable training, and broader hardware compatibility. One-step and two-step SplitMeanFlow models have been successfully deployed in large-scale speech synthesis products (such as Doubao), achieving speedups of 20x.

Implicit neural representations (INR) suffer from worsening spectral bias, which results in overly smooth solutions to the inverse problem. To deal with this problem, we propose a universal framework for processing inverse problems called High-Order Implicit Neural Representations (HOIN). By refining the traditional cascade structure to foster high-order interactions among features, HOIN enhances the model's expressive power and mitigates spectral bias through its neural tangent kernel's (NTK) strong diagonal properties, accelerating and optimizing inverse problem resolution. By analyzing the model's expression space, high-order derivatives, and the NTK matrix, we theoretically validate the feasibility of HOIN. HOIN realizes 1 to 3 dB improvements in most inverse problems, establishing a new state-of-the-art recovery quality and training efficiency, thus providing a new general paradigm for INR and paving the way for it to solve the inverse problem.

Diffusion models are relatively easy to train but require many steps to generate samples. Consistency models are far more difficult to train, but generate samples in a single step. In this paper we propose Multistep Consistency Models: A unification between Consistency Models (Song et al., 2023) and TRACT (Berthelot et al., 2023) that can interpolate between a consistency model and a diffusion model: a trade-off between sampling speed and sampling quality. Specifically, a 1-step consistency model is a conventional consistency model whereas we show that a infty-step consistency model is a diffusion model. Multistep Consistency Models work really well in practice. By increasing the sample budget from a single step to 2-8 steps, we can train models more easily that generate higher quality samples, while retaining much of the sampling speed benefits. Notable results are 1.4 FID on Imagenet 64 in 8 step and 2.1 FID on Imagenet128 in 8 steps with consistency distillation. We also show that our method scales to a text-to-image diffusion model, generating samples that are very close to the quality of the original model.

The efficiency of Federated Learning (FL) is often affected by both data and device heterogeneities. Data heterogeneity is defined as the heterogeneity of data distributions on different clients. Device heterogeneity is defined as the clients' variant latencies in uploading their local model updates due to heterogeneous conditions of local hardware resources, and causes the problem of staleness when being addressed by asynchronous FL. Traditional schemes of tackling the impact of staleness consider data and device heterogeneities as two separate and independent aspects in FL, but this assumption is unrealistic in many practical FL scenarios where data and device heterogeneities are intertwined. In these cases, traditional schemes of weighted aggregation in FL have been proved to be ineffective, and a better approach is to convert a stale model update into a non-stale one. In this paper, we present a new FL framework that leverages the gradient inversion technique for such conversion, hence efficiently tackling unlimited staleness in clients' model updates. Our basic idea is to use gradient inversion to get estimations of clients' local training data from their uploaded stale model updates, and use these estimations to compute non-stale client model updates. In this way, we address the problem of possible data quality drop when using gradient inversion, while still preserving the clients' local data privacy. We compared our approach with the existing FL strategies on mainstream datasets and models, and experiment results demonstrate that when tackling unlimited staleness, our approach can significantly improve the trained model accuracy by up to 20% and speed up the FL training progress by up to 35%.

Diffusion models have found widespread adoption in various areas. However, their sampling process is slow because it requires hundreds to thousands of network evaluations to emulate a continuous process defined by differential equations. In this work, we use neural operators, an efficient method to solve the probability flow differential equations, to accelerate the sampling process of diffusion models. Compared to other fast sampling methods that have a sequential nature, we are the first to propose parallel decoding method that generates images with only one model forward pass. We propose diffusion model sampling with neural operator (DSNO) that maps the initial condition, i.e., Gaussian distribution, to the continuous-time solution trajectory of the reverse diffusion process. To model the temporal correlations along the trajectory, we introduce temporal convolution layers that are parameterized in the Fourier space into the given diffusion model backbone. We show our method achieves state-of-the-art FID of 4.12 for CIFAR-10 and 8.35 for ImageNet-64 in the one-model-evaluation setting.

Generative modeling can be formulated as learning a mapping f such that its pushforward distribution matches the data distribution. The pushforward behavior can be carried out iteratively at inference time, for example in diffusion and flow-based models. In this paper, we propose a new paradigm called Drifting Models, which evolve the pushforward distribution during training and naturally admit one-step inference. We introduce a drifting field that governs the sample movement and achieves equilibrium when the distributions match. This leads to a training objective that allows the neural network optimizer to evolve the distribution. In experiments, our one-step generator achieves state-of-the-art results on ImageNet at 256 x 256 resolution, with an FID of 1.54 in latent space and 1.61 in pixel space. We hope that our work opens up new opportunities for high-quality one-step generation.

We introduce NitroFusion, a fundamentally different approach to single-step diffusion that achieves high-quality generation through a dynamic adversarial framework. While one-step methods offer dramatic speed advantages, they typically suffer from quality degradation compared to their multi-step counterparts. Just as a panel of art critics provides comprehensive feedback by specializing in different aspects like composition, color, and technique, our approach maintains a large pool of specialized discriminator heads that collectively guide the generation process. Each discriminator group develops expertise in specific quality aspects at different noise levels, providing diverse feedback that enables high-fidelity one-step generation. Our framework combines: (i) a dynamic discriminator pool with specialized discriminator groups to improve generation quality, (ii) strategic refresh mechanisms to prevent discriminator overfitting, and (iii) global-local discriminator heads for multi-scale quality assessment, and unconditional/conditional training for balanced generation. Additionally, our framework uniquely supports flexible deployment through bottom-up refinement, allowing users to dynamically choose between 1-4 denoising steps with the same model for direct quality-speed trade-offs. Through comprehensive experiments, we demonstrate that NitroFusion significantly outperforms existing single-step methods across multiple evaluation metrics, particularly excelling in preserving fine details and global consistency.

We provide a new theoretical framework for the variable-step deferred correction (DC) methods based on the well-known BDF2 formula. By using the discrete orthogonal convolution kernels, some high-order BDF2-DC methods are proven to be stable on arbitrary time grids according to the recent definition of stability (SINUM, 60: 2253-2272). It significantly relaxes the existing step-ratio restrictions for the BDF2-DC methods (BIT, 62: 1789-1822). The associated sharp error estimates are established by taking the numerical effects of the starting approximations into account, and they suggest that the BDF2-DC methods have no aftereffect, that is, the lower-order starting scheme for the BDF2 scheme will not cause a loss in the accuracy of the high-order BDF2-DC methods. Extensive tests on the graded and random time meshes are presented to support the new theory.

We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms. We reformulate training as a large-scale feasibility problem: finding network parameters and states that satisfy local constraints derived from its elementary operations. Training then involves projecting onto these constraints, a local operation that can be parallelized across the network. We introduce PJAX, a JAX-based software framework that enables this paradigm. PJAX composes projection operators for elementary operations, automatically deriving the solution operators for the feasibility problems (akin to autodiff for derivatives). It inherently supports GPU/TPU acceleration, provides a familiar NumPy-like API, and is extensible. We train diverse architectures (MLPs, CNNs, RNNs) on standard benchmarks using PJAX, demonstrating its functionality and generality. Our results show that this approach is as a compelling alternative to gradient-based training, with clear advantages in parallelism and the ability to handle non-differentiable operations.

MeanFlow (MF) has recently been established as a framework for one-step generative modeling. However, its ``fastforward'' nature introduces key challenges in both the training objective and the guidance mechanism. First, the original MF's training target depends not only on the underlying ground-truth fields but also on the network itself. To address this issue, we recast the objective as a loss on the instantaneous velocity v, re-parameterized by a network that predicts the average velocity u. Our reformulation yields a more standard regression problem and improves the training stability. Second, the original MF fixes the classifier-free guidance scale during training, which sacrifices flexibility. We tackle this issue by formulating guidance as explicit conditioning variables, thereby retaining flexibility at test time. The diverse conditions are processed through in-context conditioning, which reduces model size and benefits performance. Overall, our improved MeanFlow (iMF) method, trained entirely from scratch, achieves 1.72 FID with a single function evaluation (1-NFE) on ImageNet 256times256. iMF substantially outperforms prior methods of this kind and closes the gap with multi-step methods while using no distillation. We hope our work will further advance fastforward generative modeling as a stand-alone paradigm.

Most existing learning-based methods for solving imaging inverse problems can be roughly divided into two classes: iterative algorithms, such as plug-and-play and diffusion methods, that leverage pretrained denoisers, and unrolled architectures that are trained end-to-end for specific imaging problems. Iterative methods in the first class are computationally costly and often provide suboptimal reconstruction performance, whereas unrolled architectures are generally specific to a single inverse problem and require expensive training. In this work, we propose a novel non-iterative, lightweight architecture that incorporates knowledge about the forward operator (acquisition physics and noise parameters) without relying on unrolling. Our model is trained to solve a wide range of inverse problems beyond denoising, including deblurring, magnetic resonance imaging, computed tomography, inpainting, and super-resolution. The proposed model can be easily adapted to unseen inverse problems or datasets with a few fine-tuning steps (up to a few images) in a self-supervised way, without ground-truth references. Throughout a series of experiments, we demonstrate state-of-the-art performance from medical imaging to low-photon imaging and microscopy.

Recent years have witnessed the rapid progress and broad application of diffusion probabilistic models (DPMs). Sampling from DPMs can be viewed as solving an ordinary differential equation (ODE). Despite the promising performance, the generation of DPMs usually consumes much time due to the large number of function evaluations (NFE). Though recent works have accelerated the sampling to around 20 steps with high-order solvers, the sample quality with less than 10 NFE can still be improved. In this paper, we propose a unified sampling framework (USF) to study the optional strategies for solver. Under this framework, we further reveal that taking different solving strategies at different timesteps may help further decrease the truncation error, and a carefully designed solver schedule has the potential to improve the sample quality by a large margin. Therefore, we propose a new sampling framework based on the exponential integral formulation that allows free choices of solver strategy at each step and design specific decisions for the framework. Moreover, we propose S^3, a predictor-based search method that automatically optimizes the solver schedule to get a better time-quality trade-off of sampling. We demonstrate that S^3 can find outstanding solver schedules which outperform the state-of-the-art sampling methods on CIFAR-10, CelebA, ImageNet, and LSUN-Bedroom datasets. Specifically, we achieve 2.69 FID with 10 NFE and 6.86 FID with 5 NFE on CIFAR-10 dataset, outperforming the SOTA method significantly. We further apply S^3 to Stable-Diffusion model and get an acceleration ratio of 2times, showing the feasibility of sampling in very few steps without retraining the neural network.

Recent advances in continuous generative models, including multi-step approaches like diffusion and flow-matching (typically requiring 8-1000 sampling steps) and few-step methods such as consistency models (typically 1-8 steps), have demonstrated impressive generative performance. However, existing work often treats these approaches as distinct paradigms, resulting in separate training and sampling methodologies. We introduce a unified framework for training, sampling, and analyzing these models. Our implementation, the Unified Continuous Generative Models Trainer and Sampler (UCGM-{T,S}), achieves state-of-the-art (SOTA) performance. For example, on ImageNet 256x256 using a 675M diffusion transformer, UCGM-T trains a multi-step model achieving 1.30 FID in 20 steps and a few-step model reaching 1.42 FID in just 2 steps. Additionally, applying UCGM-S to a pre-trained model (previously 1.26 FID at 250 steps) improves performance to 1.06 FID in only 40 steps. Code is available at: https://github.com/LINs-lab/UCGM.

Inspired by the foundational works by Spivak and Fong and Cruttwell et al., we introduce a categorical framework to formalize Bayesian inference and learning. The two key ideas at play here are the notions of Bayesian inversions and the functor GL as constructed by Cruttwell et al.. In this context, we find that Bayesian learning is the simplest case of the learning paradigm. We then obtain categorical formulations of batch and sequential Bayes updates while also verifying that the two coincide in a specific example.

Diffusion models have achieved remarkable success in imaging inverse problems owing to their powerful generative capabilities. However, existing approaches typically rely on models trained for specific degradation types, limiting their generalizability to various degradation scenarios. To address this limitation, we propose a zero-shot framework capable of handling various imaging inverse problems without model retraining. We introduce a likelihood-guided noise refinement mechanism that derives a closed-form approximation of the likelihood score, simplifying score estimation and avoiding expensive gradient computations. This estimated score is subsequently utilized to refine the model-predicted noise, thereby better aligning the restoration process with the generative framework of diffusion models. In addition, we integrate the Denoising Diffusion Implicit Models (DDIM) sampling strategy to further improve inference efficiency. The proposed mechanism can be applied to both optimization-based and sampling-based schemes, providing an effective and flexible zero-shot solution for imaging inverse problems. Extensive experiments demonstrate that our method achieves superior performance across multiple inverse problems, particularly in compressive sensing, delivering high-quality reconstructions even at an extremely low sampling rate (5%).

Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic differentiation algorithms that also includes the forward mode. We present a method to compute gradients based solely on the directional derivative that one can compute exactly and efficiently via the forward mode. We call this formulation the forward gradient, an unbiased estimate of the gradient that can be evaluated in a single forward run of the function, entirely eliminating the need for backpropagation in gradient descent. We demonstrate forward gradient descent in a range of problems, showing substantial savings in computation and enabling training up to twice as fast in some cases.

Recent work in probability-domain knowledge distillation has established axiomatic frameworks for temperature scaling, multi-teacher aggregation, and bias-variance trade-offs in single-stage settings. However, the mathematical behavior of recursive or multi-generation distillation remains poorly understood, with prior approaches relying primarily on empirical heuristics. In this work, we introduce an axiomatic and operator-theoretic framework for recursive meta-distillation, formalizing iterative knowledge distillation as a sequence of probability-distribution operators with explicit anchoring to base teachers. We define structural axioms for valid meta-teacher construction and prove the existence of non-trivial operator families satisfying these axioms without specifying particular algorithms or loss functions. Under mild realizability and convexity assumptions, we show that anchored recursive distillation induces contraction in KL divergence, yielding geometric convergence to base teacher distributions and a unique, globally attractive fixed point. The contribution is foundational rather than algorithmic: the framework characterizes when recursive distillation is mathematically well-posed and convergent rather than error-accumulating, independent of model architecture, optimization details, or specific operator instantiations. These results provide a theoretical basis for understanding stability, bias-variance behavior, and failure modes in iterative and multi-teacher distillation under capacity constraints.

Recent advancements in latent diffusion models (LDMs) have markedly enhanced text-to-audio generation, yet their iterative sampling processes impose substantial computational demands, limiting practical deployment. While recent methods utilizing consistency-based distillation aim to achieve few-step or single-step inference, their one-step performance is constrained by curved trajectories, preventing them from surpassing traditional diffusion models. In this work, we introduce FlashAudio with rectified flows to learn straight flow for fast simulation. To alleviate the inefficient timesteps allocation and suboptimal distribution of noise, FlashAudio optimizes the time distribution of rectified flow with Bifocal Samplers and proposes immiscible flow to minimize the total distance of data-noise pairs in a batch vias assignment. Furthermore, to address the amplified accumulation error caused by the classifier-free guidance (CFG), we propose Anchored Optimization, which refines the guidance scale by anchoring it to a reference trajectory. Experimental results on text-to-audio generation demonstrate that FlashAudio's one-step generation performance surpasses the diffusion-based models with hundreds of sampling steps on audio quality and enables a sampling speed of 400x faster than real-time on a single NVIDIA 4090Ti GPU.

Neural networks are famously nonlinear. However, linearity is defined relative to a pair of vector spaces, f:XtoY. Is it possible to identify a pair of non-standard vector spaces for which a conventionally nonlinear function is, in fact, linear? This paper introduces a method that makes such vector spaces explicit by construction. We find that if we sandwich a linear operator A between two invertible neural networks, f(x)=g_y^{-1}(A g_x(x)), then the corresponding vector spaces X and Y are induced by newly defined addition and scaling actions derived from g_x and g_y. We term this kind of architecture a Linearizer. This framework makes the entire arsenal of linear algebra, including SVD, pseudo-inverse, orthogonal projection and more, applicable to nonlinear mappings. Furthermore, we show that the composition of two Linearizers that share a neural network is also a Linearizer. We leverage this property and demonstrate that training diffusion models using our architecture makes the hundreds of sampling steps collapse into a single step. We further utilize our framework to enforce idempotency (i.e. f(f(x))=f(x)) on networks leading to a globally projective generative model and to demonstrate modular style transfer.

A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general solution to a longstanding open problem relevant to a wide variety of applications in robotics, tracking, and control systems. The new inverse complements the Drazin inverse (which is consistent with respect to similarity transformations) and the Moore-Penrose inverse (which is consistent with respect to unitary/orthonormal transformations) to complete a trilogy of generalized matrix inverses that exhausts the standard family of analytically-important linear system transformations. Results are generalized to obtain unit-consistent and unit-invariant matrix decompositions and examples of their use are described.

The Mechanistic Interpretability (MI) program has mapped the Transformer as a precise computational graph. We extend this graph with a conservation law and time-varying AC dynamics, viewing it as a physical circuit. We introduce Momentum Attention, a symplectic augmentation embedding physical priors via the kinematic difference operator p_t = q_t - q_{t-1}, implementing the symplectic shear q_t = q_t + γp_t on queries and keys. We identify a fundamental Symplectic-Filter Duality: the physical shear is mathematically equivalent to a High-Pass Filter. This duality is our cornerstone contribution -- by injecting kinematic momentum, we sidestep the topological depth constraint (L geq 2) for induction head formation. While standard architectures require two layers for induction from static positions, our extension grants direct access to velocity, enabling Single-Layer Induction and Spectral Forensics via Bode Plots. We formalize an Orthogonality Theorem proving that DC (semantic) and AC (mechanistic) signals segregate into orthogonal frequency bands when Low-Pass RoPE interacts with High-Pass Momentum. Validated through 5,100+ controlled experiments (documented in Supplementary Appendices A--R and 27 Jupyter notebooks), our 125M Momentum model exceeds expectations on induction-heavy tasks while tracking a 350M baseline within sim2.9% validation loss. Dedicated associative recall experiments reveal a scaling law γ^* = 4.17 times N^{-0.74} establishing momentum-depth fungibility. We offer this framework as a complementary analytical toolkit connecting Generative AI, Hamiltonian Physics, and Signal Processing.

This paper addresses the societal concerns arising from large-scale text-to-image diffusion models for generating potentially harmful or copyrighted content. Existing models rely heavily on internet-crawled data, wherein problematic concepts persist due to incomplete filtration processes. While previous approaches somewhat alleviate the issue, they often rely on text-specified concepts, introducing challenges in accurately capturing nuanced concepts and aligning model knowledge with human understandings. In response, we propose a framework named Human Feedback Inversion (HFI), where human feedback on model-generated images is condensed into textual tokens guiding the mitigation or removal of problematic images. The proposed framework can be built upon existing techniques for the same purpose, enhancing their alignment with human judgment. By doing so, we simplify the training objective with a self-distillation-based technique, providing a strong baseline for concept removal. Our experimental results demonstrate our framework significantly reduces objectionable content generation while preserving image quality, contributing to the ethical deployment of AI in the public sphere.

We propose a new score-based model with one-step sampling. Previously, score-based models were burdened with heavy computations due to iterative sampling. For substituting the iterative process, we train a standalone generator to compress all the time steps with the gradient backpropagated from the score network. In order to produce meaningful gradients for the generator, the score network is trained to simultaneously match the real data distribution and mismatch the fake data distribution. This model has the following advantages: 1) For sampling, it generates a fake image with only one step forward. 2) For training, it only needs 10 diffusion steps.3) Compared with consistency model, it is free of the ill-posed problem caused by consistency loss. On the popular CIFAR-10 dataset, our model outperforms Consistency Model and Denoising Score Matching, which demonstrates the potential of the framework. We further provide more examples on the MINIST and LSUN datasets. The code is available on GitHub.

Evaluating natural language generation (NLG) systems is challenging due to the diversity of valid outputs. While human evaluation is the gold standard, it suffers from inconsistencies, lack of standardisation, and demographic biases, limiting reproducibility. LLM-based evaluation offers a scalable alternative but is highly sensitive to prompt design, where small variations can lead to significant discrepancies. In this work, we propose an inversion learning method that learns effective reverse mappings from model outputs back to their input instructions, enabling the automatic generation of highly effective, model-specific evaluation prompts. Our method requires only a single evaluation sample and eliminates the need for time-consuming manual prompt engineering, thereby improving both efficiency and robustness. Our work contributes toward a new direction for more robust and efficient LLM-based evaluation.