---
license: mit
library_name: diffusers
pipeline_tag: text-to-image
---

<h1 align="center">
  Continuous-Time Distribution Matching for Few-Step Diffusion Distillation
</h1>

<div align="center">

<a href="https://byliutao.github.io/cdm_page/">
    <img src="https://img.shields.io/badge/Project_Page-0055b3?logo=githubpages&logoColor=white" alt="Project Page">
</a>
<a href="https://huggingface.co/byliutao/stable-diffusion-3-medium-turbo">
    <img src="https://img.shields.io/badge/%F0%9F%A4%97%20Model-SD3_Medium-ffc107" alt="SD3-Medium Model">
</a>
<a href="https://huggingface.co/byliutao/Longcat-Image-Turbo">
    <img src="https://img.shields.io/badge/%F0%9F%A4%97%20Model-LongCat-ffc107" alt="LongCat Model">
</a>
<a href="https://github.com/byliutao/cdm">
    <img src="https://img.shields.io/badge/GitHub-byliutao%2Fcdm-black?logo=github&logoColor=white" alt="GitHub">
</a>
<a href="https://huggingface.co/papers/2605.06376">
    <img src="https://img.shields.io/badge/Paper-2605.06376-b31b1b?logo=arxiv&logoColor=white" alt="Paper">
</a>

</div>

This repository contains the weights for Longcat-Image-Turbo, a few-step distilled version of Longcat-Image using the **Continuous-Time Distribution Matching (CDM)** method presented in [Continuous-Time Distribution Matching for Few-Step Diffusion Distillation](https://huggingface.co/papers/2605.06376).

CDM migrates the Distribution Matching Distillation (DMD) framework from discrete anchoring to continuous optimization, allowing for high-quality image generation with very few steps (e.g., 4 NFE).

<p align="center">
  <a href="#algorithm-overview">Algorithm Overview</a> •
  <a href="#4-nfe-generation-results">Results</a> •
  <a href="#inference">Inference</a> •
  <a href="#training">Training</a> •
  <a href="#evaluation">Evaluation</a> •
  <a href="#citation">Citation</a>
</p>

<p align="center">
  <img src="assets/teaser.png" width="95%" alt="Teaser: High-quality images generated with only 4 NFE">
</p>

## Algorithm Overview

<p align="center">
  <img src="assets/pipe.png" width="90%" alt="Pipeline overview of Continuous-Time Distribution Matching">
</p>

**Overview of Continuous-Time Distribution Matching (CDM).** **Top:** Our approach employs a dynamic continuous time schedule during backward simulation, sampling intermediate anchors uniformly from (0, 1]. **Bottom Left:** CFG augmentation (CA) and distribution matching (DM) operate on this dynamic schedule to align text-image conditions and data distributions at on-trajectory anchors. **Bottom Right:** To address inter-anchor inconsistency, the proposed CDM objective explicitly extrapolates off-trajectory latents using the predicted velocity.

## 4-NFE Generation Results

### SD3-Medium

<p align="center">
  <img src="assets/sd3.png" width="90%" alt="SD3.5-Medium 4-NFE generation samples">
</p>

### LongCat

<p align="center">
  <img src="assets/longcat.png" width="90%" alt="LongCat 4-NFE generation samples">
</p>

---

## Inference

To use this model, please refer to the [GitHub repository](https://github.com/byliutao/cdm).

```bash
# Clone this repository
git clone https://github.com/byliutao/cdm.git
cd cdm

# Create and activate the inference environment
conda create -n cdm_infer python=3.10
conda activate cdm_infer
pip install -r config/requirements_infer.txt

# Run inference
python scripts/infer/longcat.py # LongCat
```

## Training

```bash
# Create and activate the training environment
conda create -n cdm_train python=3.10
conda activate cdm_train
pip install -r config/requirements_train.txt

# Launch training with FSDP2
accelerate launch --config_file config/accelerate_fsdp2.yaml \
    --num_processes 8 -m scripts.train \
    --config config/config.py:longcat  # LongCat
```

## License

This project is licensed under the MIT License — see the [LICENSE](LICENSE) file for details.

## Citation

If our work assists your research, please consider giving us a star ⭐ or citing us:

```bibtex
@misc{liu2026continuoustimedistributionmatchingfewstep,
      title={Continuous-Time Distribution Matching for Few-Step Diffusion Distillation}, 
      author={Tao Liu and Hao Yan and Mengting Chen and Taihang Hu and Zhengrong Yue and Zihao Pan and Jinsong Lan and Xiaoyong Zhu and Ming-Ming Cheng and Bo Zheng and Yaxing Wang},
      year={2026},
      eprint={2605.06376},
      archivePrefix={arXiv},
      primaryClass={cs.CV},
      url={https://arxiv.org/abs/2605.06376}, 
}
```