# SGMD: Score Gradient Matching Distillation for Few-Step Video Diffusion Distillation

arXiv: https://arxiv.org/abs/2605.30116 · HTML: https://mlsanity.com/paper/2605.30116/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 35 of its 43 references that are in the map.
- First posted on arXiv 28 May 2026.

## Placed in

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

## Builds on (most cited first, 30 of 35)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [VBench: Comprehensive Benchmark Suite for Video Generative Models](https://mlsanity.com/paper/2311.17982/) (2023)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (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)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [DeepCache: Accelerating Diffusion Models for Free](https://mlsanity.com/paper/2312.00858/) (2023)
- [Improving Video Generation with Human Feedback](https://mlsanity.com/paper/2501.13918/) (2025)
- [Unifying Flow, Stereo and Depth Estimation](https://mlsanity.com/paper/2211.05783/) (2022)
- [Timestep Embedding Tells: It's Time to Cache for Video Diffusion Model](https://mlsanity.com/paper/2411.19108/) (2024)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation](https://mlsanity.com/paper/2404.04057/) (2024)
- [R3Det: Refined Single-Stage Detector with Feature Refinement for Rotating Object](https://mlsanity.com/paper/1908.05612/) (2019)
- [HunyuanVideo 1.5 Technical Report](https://mlsanity.com/paper/2511.18870/) (2025)
- [FasterCache: Training-Free Video Diffusion Model Acceleration with High Quality](https://mlsanity.com/paper/2410.19355/) (2024)
- [Parallel Sampling of Diffusion Models](https://mlsanity.com/paper/2305.16317/) (2023)
- [Large Scale Diffusion Distillation via Score-Regularized Continuous-Time Consistency](https://mlsanity.com/paper/2510.08431/) (2025)
- [LongCat-Video Technical Report](https://mlsanity.com/paper/2510.22200/) (2025)
- [Deep Spectral Clustering using Dual Autoencoder Network](https://mlsanity.com/paper/1904.13113/) (2019)
- [One-Step Diffusion Distillation through Score Implicit Matching](https://mlsanity.com/paper/2410.16794/) (2024)
- [TFMQ-DM: Temporal Feature Maintenance Quantization for Diffusion Models](https://mlsanity.com/paper/2311.16503/) (2023)
- [A Survey of Low-bit Large Language Models: Basics, Systems, and Algorithms](https://mlsanity.com/paper/2409.16694/) (2024)
- [Self-Supervised Adversarial Hashing Networks for Cross-Modal Retrieval](https://mlsanity.com/paper/1804.01223/) (2018)
- [PipeFusion: Patch-level Pipeline Parallelism for Diffusion Transformers Inference](https://mlsanity.com/paper/2405.14430/) (2024)
- [Triplet-Based Deep Hashing Network for Cross-Modal Retrieval](https://mlsanity.com/paper/1904.02449/) (2019)
- [Phased DMD: Few-step Distribution Matching Distillation via Score Matching within Subintervals](https://mlsanity.com/paper/2510.27684/) (2025)

## Built on by (most cited first, 6 of 6)

- [DistillAlign: Coordinating Mode Covering and Mode Seeking in Autoregressive Video Distillation](https://mlsanity.com/paper/2607.26811/) (2026)
- [AptAvatar: Fast and Vivid Long-Form Audio-Driven Video Generation for Production-Ready Avatars](https://mlsanity.com/paper/2607.24013/) (2026)
- [ViRDM: Taming Representation Distribution Matching for Few-Step Causal Video Generation](https://mlsanity.com/paper/2609.28923/) (2026)
- [PDMD: Projected Distribution Matching Distillation for Video Diffusion Models](https://mlsanity.com/paper/2609.35768/) (2026)
- [Self-Aligned Forcing: Streaming Video Diffusion with Differentiable Noisy History](https://mlsanity.com/paper/2609.38114/) (2026)
- [DMAD: Distribution Matching as Adversarial Distillation for Fast Visual Generation](https://mlsanity.com/paper/2610.02188/) (2026)

## Abstract (arXiv)

Distribution Matching Distillation (DMD) is a widely used paradigm for accelerating inference in few-step video diffusion models. However, DMD-style video distillation faces two coupled challenges: the fake score must track a continuously evolving generator, making training costly when frequent updates are required, while reverse-KL-style matching can be mode-seeking and conservative for preserving strong motion dynamics. To address these issues, we propose Score Gradient Matching Distillation (SGMD). SGMD adopts a fake-score perspective by directly optimizing the fake score toward the teacher, while using teacher stop-gradient Fisher as a stable distribution-matching objective. We provide a gradient analysis that motivates this objective choice under ideal tracking. Building on this, SGMD introduces a pair of dual potentials: negative-residual (NR) for outer-loop correction and residual-contraction (RC) for inner-loop tracking. Empirically, compared to DMD2, SGMD achieves an approximately ~ 3× training speedup and substantially improves motion dynamics for 4-step distilled models while preserving temporal consistency. A human study confirms that SGMD is preferred in motion quality and overall preference, while visual quality and text alignment remain comparable. Code is available at https://github.com/ModelTC/LightX2V.