# Learning Few-Step Diffusion Models by Trajectory Distribution Matching

arXiv: https://arxiv.org/abs/2503.06674 · HTML: https://mlsanity.com/paper/2503.06674/

## Key facts

- Cited by 57 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 41 references that are in the map.
- First posted on arXiv 9 Mar 2025.

## 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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [CogVideoX: Text-to-Video Diffusion Models with An Expert Transformer](https://mlsanity.com/paper/2408.06072/) (2024)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [VBench: Comprehensive Benchmark Suite for Video Generative Models](https://mlsanity.com/paper/2311.17982/) (2023)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [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)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models](https://mlsanity.com/paper/2305.18455/) (2023)
- [Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation](https://mlsanity.com/paper/2404.04057/) (2024)
- [LCM-LoRA: A Universal Stable-Diffusion Acceleration Module](https://mlsanity.com/paper/2311.05556/) (2023)
- [UFOGen: You Forward Once Large Scale Text-to-Image Generation via Diffusion GANs](https://mlsanity.com/paper/2311.09257/) (2023)
- [Hyper-SD: Trajectory Segmented Consistency Model for Efficient Image Synthesis](https://mlsanity.com/paper/2404.13686/) (2024)

## Built on by (most cited first, 30 of 57)

- [Self-Forcing++: Towards Minute-Scale High-Quality Video Generation](https://mlsanity.com/paper/2510.02283/) (2025)
- [Kling-Omni Technical Report](https://mlsanity.com/paper/2512.16776/) (2025)
- [Distribution Matching Distillation Meets Reinforcement Learning](https://mlsanity.com/paper/2511.13649/) (2025)
- [DiffusionOPD: A Unified Perspective of On-Policy Distillation in Diffusion Models](https://mlsanity.com/paper/2605.15055/) (2026)
- [Phased DMD: Few-step Distribution Matching Distillation via Score Matching within Subintervals](https://mlsanity.com/paper/2510.27684/) (2025)
- [D-OPSD: On-Policy Self-Distillation for Continuously Tuning Step-Distilled Diffusion Models](https://mlsanity.com/paper/2605.05204/) (2026)
- [Diversity-Preserved Distribution Matching Distillation for Fast Visual Synthesis](https://mlsanity.com/paper/2602.03139/) (2026)
- [Reward-Instruct: A Reward-Centric Approach to Fast Photo-Realistic Image Generation](https://mlsanity.com/paper/2503.13070/) (2025)
- [Reinforcing Diffusion Models by Direct Group Preference Optimization](https://mlsanity.com/paper/2510.08425/) (2025)
- [BLADE: Block-Sparse Attention Meets Step Distillation for Efficient Video Generation](https://mlsanity.com/paper/2508.10774/) (2025)
- [Hallo-Live: Real-Time Streaming Joint Audio-Video Avatar Generation with Asynchronous Dual-Stream and Human-Centric Preference Distillation](https://mlsanity.com/paper/2604.23632/) (2026)
- [Ideas in Inference-time Scaling can Benefit Generative Pre-training Algorithms](https://mlsanity.com/paper/2503.07154/) (2025)
- [Reinforcing Few-step Generators via Reward-Tilted Distribution Matching](https://mlsanity.com/paper/2605.26108/) (2026)
- [TDM-R1: Reinforcing Few-Step Diffusion Models with Non-Differentiable Reward](https://mlsanity.com/paper/2603.07700/) (2026)
- [Adaptive Video Distillation: Mitigating Oversaturation and Temporal Collapse in Few-Step Generation](https://mlsanity.com/paper/2603.21864/) (2026)
- [Efficient Video Diffusion Models: Advancements and Challenges](https://mlsanity.com/paper/2604.15911/) (2026)
- [Soft-Di[M]O: Improving One-Step Discrete Image Generation with Soft Embeddings](https://mlsanity.com/paper/2509.22925/) (2025)
- [An Empirical Study of Training Pixel-Space Text-to-Image Diffusion Models](https://mlsanity.com/paper/2608.16887/) (2026)
- [PSA: Pyramid Sparse Attention for Efficient Video Understanding and Generation](https://mlsanity.com/paper/2512.04025/) (2025)
- [Just-in-Time: Training-Free Spatial Acceleration for Diffusion Transformers](https://mlsanity.com/paper/2603.10744/) (2026)
- [1.x-Distill: Breaking the Diversity, Quality, and Efficiency Barrier in Distribution Matching Distillation](https://mlsanity.com/paper/2604.04018/) (2026)
- [Continuous-Time Distribution Matching for Few-Step Diffusion Distillation](https://mlsanity.com/paper/2605.06376/) (2026)
- [Noise Consistency Training: A Native Approach for One-Step Generator in Learning Additional Controls](https://mlsanity.com/paper/2506.19741/) (2025)
- [From Structure to Detail: Hierarchical Distillation for Efficient Diffusion Model](https://mlsanity.com/paper/2511.08930/) (2025)
- [When Distillation Breaks Motion Control: Restoring Generative Trajectories for Fast Video Generators](https://mlsanity.com/paper/2506.19348/) (2025)
- [Live Avatar: Streaming Real-time Audio-Driven Avatar Generation with Infinite Length](https://mlsanity.com/paper/2512.04677/) (2025)
- [Guiding Distribution Matching Distillation with Gradient-Based Reinforcement Learning](https://mlsanity.com/paper/2604.19009/) (2026)
- [DefaultShift: Auditing Semantic Default Shift in Accelerated Text-to-Image Models](https://mlsanity.com/paper/2608.21784/) (2026)
- [Cross-Resolution Distribution Matching for Diffusion Distillation](https://mlsanity.com/paper/2603.06136/) (2026)
- [EruDiff: Refactoring Knowledge in Diffusion Models for Advanced Text-to-Image Synthesis](https://mlsanity.com/paper/2603.20828/) (2026)

## Abstract (arXiv)

Accelerating diffusion model sampling is crucial for efficient AIGC deployment. While diffusion distillation methods -- based on distribution matching and trajectory matching -- reduce sampling to as few as one step, they fall short on complex tasks like text-to-image generation. Few-step generation offers a better balance between speed and quality, but existing approaches face a persistent trade-off: distribution matching lacks flexibility for multi-step sampling, while trajectory matching often yields suboptimal image quality. To bridge this gap, we propose learning few-step diffusion models by Trajectory Distribution Matching (TDM), a unified distillation paradigm that combines the strengths of distribution and trajectory matching. Our method introduces a data-free score distillation objective, aligning the student's trajectory with the teacher's at the distribution level. Further, we develop a sampling-steps-aware objective that decouples learning targets across different steps, enabling more adjustable sampling. This approach supports both deterministic sampling for superior image quality and flexible multi-step adaptation, achieving state-of-the-art performance with remarkable efficiency. Our model, TDM, outperforms existing methods on various backbones, such as SDXL and PixArt-α, delivering superior quality and significantly reduced training costs. In particular, our method distills PixArt-α into a 4-step generator that outperforms its teacher on real user preference at 1024 resolution. This is accomplished with 500 iterations and 2 A800 hours -- a mere 0.01% of the teacher's training cost. In addition, our proposed TDM can be extended to accelerate text-to-video diffusion. Notably, TDM can outperform its teacher model (CogVideoX-2B) by using only 4 NFE on VBench, improving the total score from 80.91 to 81.65. Project page: https://tdm-t2x.github.io/