# Distribution Matching Distillation without Fake Score Network

arXiv: https://arxiv.org/abs/2605.19256 · HTML: https://mlsanity.com/paper/2605.19256/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 30 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 26 of 26)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [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)
- [Reconstruction vs. Generation: Taming Optimization Dilemma in Latent Diffusion Models](https://mlsanity.com/paper/2501.01423/) (2025)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [Improved Mean Flows: On the Challenges of Fastforward Generative Models](https://mlsanity.com/paper/2512.02012/) (2025)
- [Flow map matching with stochastic interpolants: A mathematical framework for consistency models](https://mlsanity.com/paper/2406.07507/) (2024)
- [Align Your Flow: Scaling Continuous-Time Flow Map Distillation](https://mlsanity.com/paper/2506.14603/) (2025)
- [Large Scale Diffusion Distillation via Score-Regularized Continuous-Time Consistency](https://mlsanity.com/paper/2510.08431/) (2025)
- [Multistep Distillation of Diffusion Models via Moment Matching](https://mlsanity.com/paper/2406.04103/) (2024)
- [Adversarial Distribution Matching for Diffusion Distillation Towards Efficient Image and Video Synthesis](https://mlsanity.com/paper/2507.18569/) (2025)
- [SenseFlow: Scaling Distribution Matching for Flow-based Text-to-Image Distillation](https://mlsanity.com/paper/2506.00523/) (2025)
- [Decoupled MeanFlow: Turning Flow Models into Flow Maps for Accelerated Sampling](https://mlsanity.com/paper/2510.24474/) (2025)
- [TwinFlow: Realizing One-step Generation on Large Models with Self-adversarial Flows](https://mlsanity.com/paper/2512.05150/) (2025)
- [Transition Matching: Scalable and Flexible Generative Modeling](https://mlsanity.com/paper/2506.23589/) (2025)

## Built on by (most cited first, 4 of 4)

- [Distilling Drifting Transformers with Representation Autoencoders](https://mlsanity.com/paper/2606.15553/) (2026)
- [Elucidating the Design Space of Regression-based Diffusion Reinforcement Learning](https://mlsanity.com/paper/2609.33444/) (2026)
- [PDMD: Projected Distribution Matching Distillation for Video Diffusion Models](https://mlsanity.com/paper/2609.35768/) (2026)
- [DMAD: Distribution Matching as Adversarial Distillation for Fast Visual Generation](https://mlsanity.com/paper/2610.02188/) (2026)

## Abstract (arXiv)

Distribution Matching Distillation (DMD) provides an effective distribution-level correction for few-step generation, while relying on an auxiliary fake-score network to track the evolving generative distribution. Recent work combines DMD-style objectives with flow-map generators to exploit both forward-divergence training and reverse-divergence correction. The fake-score estimator remains an additional component with memory and update overhead. In this work, we study whether this explicit tracker can be avoided when the generator itself has a flow-map structure. We propose Fake-Score-network-Free DMD (FSF-DMD), a DMD formulation for flow-map generators that replaces the auxiliary fake-score estimator with a generator-induced pseudo-velocity surrogate. The key observation is that the endpoint pseudo-velocity of a flow-map generator provides a tractable proxy for fake-velocity estimation, allowing the generator itself to supply the reverse-divergence signal. Building on this observation, we derive a practical objective, extend it with flow-map-consistent backward simulation, and introduce a self-teacher variant for training from scratch. In our ImageNet-1K 256 × 256 experiments, FSF-DMD improves flow-map baselines, reaches lower FID than the listed DMD2 comparisons in the flow-map-initialized setting, and remains effective under flow-matching initialization and training from scratch.