# Score Distillation of Flow Matching Models arXiv: https://arxiv.org/abs/2509.25127 ยท HTML: https://mlsanity.com/paper/2509.25127/ ## Key facts - Cited by 8 papers in the map (data through 14 Oct 2026). - Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. - Builds on 56 of its 63 references that are in the map. - First posted on arXiv 29 Sep 2025. ## Placed in - Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/) ## Builds on (most cited first, 30 of 56) - [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021) - [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020) - [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) - [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022) - [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022) - [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022) - [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024) - [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019) - [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022) - [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022) - [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022) - [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) - [LAION-400M: Open Dataset of CLIP-Filtered 400 Million Image-Text Pairs](https://mlsanity.com/paper/2111.02114/) (2021) - [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023) - [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023) - [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023) - [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023) - [GenEval: An Object-Focused Framework for Evaluating Text-to-Image Alignment](https://mlsanity.com/paper/2310.11513/) (2023) - [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023) - [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) - [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023) - [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024) - [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022) - [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022) - [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024) - [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022) ## Built on by (most cited first, 8 of 8) - [Mean Flow Distillation: Robust and Stable Distillation for Flow Matching Models](https://mlsanity.com/paper/2606.11155/) (2026) - [Preconditioned Flow Matching](https://mlsanity.com/paper/2603.02337/) (2026) - [StAD: Stein Amortized Divergence for Fast Likelihoods with Diffusion and Flow](https://mlsanity.com/paper/2605.16486/) (2026) - [Restoring Initial Noise Sensitivity in Text-to-Image Distillation via Geometric Alignment](https://mlsanity.com/paper/2606.01651/) (2026) - [RoamFlow: Reinforcement-Aligned One-Step Action MeanFlow Policy for Image-Goal Navigation](https://mlsanity.com/paper/2606.29934/) (2026) - [PFM-HR: Pose Flow Matching for Humanoid Robots](https://mlsanity.com/paper/2608.03227/) (2026) - [Visualizing Distribution Coverage in Generative Diffusion Models](https://mlsanity.com/paper/2609.38853/) (2026) - [Few-Step Generation via Data-Space Iteration](https://mlsanity.com/paper/2610.12102/) (2026) ## Abstract (arXiv) Diffusion models achieve high-quality image generation but are limited by slow iterative sampling. Distillation methods alleviate this by enabling one- or few-step generation. Flow matching, originally introduced as a distinct framework, has since been shown to be theoretically equivalent to diffusion under Gaussian assumptions, raising the question of whether distillation techniques such as score distillation transfer directly. We provide a simple derivation -- based on Bayes' rule and conditional expectations -- that unifies Gaussian diffusion and flow matching without relying on ODE/SDE formulations. Building on this view, we extend Score identity Distillation (SiD) to pretrained text-to-image flow-matching models, including SANA, SD3-Medium, SD3.5-Medium/Large, and FLUX.1-dev, all with DiT backbones. Experiments show that, with only modest flow-matching- and DiT-specific adjustments, SiD works out of the box across these models, in both data-free and data-aided settings, without requiring teacher finetuning or architectural changes. This provides the first systematic evidence that score distillation applies broadly to text-to-image flow matching models, resolving prior concerns about stability and soundness and unifying acceleration techniques across diffusion- and flow-based generators. A project page is available at https://yigu1008.github.io/SiD-DiT.