# PDMD: Projected Distribution Matching Distillation for Video Diffusion Models

arXiv: https://arxiv.org/abs/2609.35768 · HTML: https://mlsanity.com/paper/2609.35768/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 47 of its 55 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 47)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [VBench: Comprehensive Benchmark Suite for Video Generative Models](https://mlsanity.com/paper/2311.17982/) (2023)
- [ImageBind: One Embedding Space To Bind Them All](https://mlsanity.com/paper/2305.05665/) (2023)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [WorldSimBench: Towards Video Generation Models as World Simulators](https://mlsanity.com/paper/2410.18072/) (2024)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [Self Forcing: Bridging the Train-Test Gap in Autoregressive Video Diffusion](https://mlsanity.com/paper/2506.08009/) (2025)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [Fast High-Resolution Image Synthesis with Latent Adversarial Diffusion Distillation](https://mlsanity.com/paper/2403.12015/) (2024)
- [SDXL-Lightning: Progressive Adversarial Diffusion Distillation](https://mlsanity.com/paper/2402.13929/) (2024)
- [Seedance 1.0: Exploring the Boundaries of Video Generation Models](https://mlsanity.com/paper/2506.09113/) (2025)
- [Efficient Training of Audio Transformers with Patchout](https://mlsanity.com/paper/2110.05069/) (2021)
- [FlowEdit: Inversion-Free Text-Based Editing Using Pre-Trained Flow Models](https://mlsanity.com/paper/2412.08629/) (2024)
- [Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation](https://mlsanity.com/paper/2404.04057/) (2024)
- [UFOGen: You Forward Once Large Scale Text-to-Image Generation via Diffusion GANs](https://mlsanity.com/paper/2311.09257/) (2023)
- [Diffusion Adversarial Post-Training for One-Step Video Generation](https://mlsanity.com/paper/2501.08316/) (2025)
- [Re-imagine the Negative Prompt Algorithm: Transform 2D Diffusion into 3D, alleviate Janus problem and Beyond](https://mlsanity.com/paper/2304.04968/) (2023)
- [Meta Audiobox Aesthetics: Unified Automatic Quality Assessment for Speech, Music, and Sound](https://mlsanity.com/paper/2502.05139/) (2025)
- [MMAudio: Taming Multimodal Joint Training for High-Quality Video-to-Audio Synthesis](https://mlsanity.com/paper/2412.15322/) (2024)
- [VidProM: A Million-scale Real Prompt-Gallery Dataset for Text-to-Video Diffusion Models](https://mlsanity.com/paper/2403.06098/) (2024)
- [Delta Denoising Score](https://mlsanity.com/paper/2304.07090/) (2023)
- [Eliminating Oversaturation and Artifacts of High Guidance Scales in Diffusion Models](https://mlsanity.com/paper/2410.02416/) (2024)
- [Synchformer: Efficient Synchronization from Sparse Cues](https://mlsanity.com/paper/2401.16423/) (2024)

## Abstract (arXiv)

Modern video diffusion models require tens of denoising evaluations over long spatiotemporal token sequences. Distribution Matching Distillation (DMD) reduces the number of function evaluations (NFE) to just a few. However, DMD samples can degrade during training, exhibiting progressive oversaturation and artifacts. We trace this instability to critic errors, which enter successive student updates and accumulate over time. We introduce Projected Distribution Matching Distillation (PDMD) to filter critic errors. PDMD projects out the component of the DMD update parallel to the student-critic endpoint residual. At a fixed noisy query, we prove that this residual is an unbiased estimate of the critic's endpoint error. Under high-dimensional assumptions, this projection removes a constant fraction of critic error while discarding only a vanishing fraction of ideal DMD signal. Empirically, the projection stabilizes training and improves sample quality where DMD degrades and develops unnatural textures. PDMD requires only a one-line code change to DMD, with no extra loss, network, data, model pass, or multi-stage training. With Wan2.1, PDMD achieves a VBench total score of 83.73 at 4 NFE, surpassing matched DMD by 1.03 points. On MiniMax-H3 joint video-audio generation, PDMD achieves a VideoGen-Eval visual total score of 83.17, 0.41 points above the strongest distilled baseline. PDMD also achieves the best performance on all six audio metrics among the compared 4-NFE models. Qualitative comparisons and user studies favor PDMD over the distilled baselines in visual quality, motion, and audio quality. Code and models are available at https://pdmd2026.github.io/.