# Bellman Optimal Stepsize Straightening of Flow-Matching Models arXiv: https://arxiv.org/abs/2312.16414 ยท HTML: https://mlsanity.com/paper/2312.16414/ ## Key facts - Cited by 11 papers in the map (data through 14 Oct 2026). - Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. - Builds on 26 of its 33 references that are in the map. - First posted on arXiv 27 Dec 2023. ## Placed in - Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/) ## Builds on (most cited first, 26 of 26) - [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) - [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022) - [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022) - [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022) - [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018) - [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) - [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017) - [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) - [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015) - [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022) - [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) - [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022) - [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023) - [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022) - [DPM-Solver-v3: Improved Diffusion ODE Solver with Empirical Model Statistics](https://mlsanity.com/paper/2310.13268/) (2023) - [Learning to Efficiently Sample from Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.03802/) (2021) - [Action Matching: Learning Stochastic Dynamics from Samples](https://mlsanity.com/paper/2210.06662/) (2022) - [AutoDiffusion: Training-Free Optimization of Time Steps and Architectures for Automated Diffusion Model Acceleration](https://mlsanity.com/paper/2309.10438/) (2023) - [Quasi-Taylor Samplers for Diffusion Generative Models based on Ideal Derivatives](https://mlsanity.com/paper/2112.13339/) (2021) ## Built on by (most cited first, 11 of 11) - [Lumina-Next: Making Lumina-T2X Stronger and Faster with Next-DiT](https://mlsanity.com/paper/2406.18583/) (2024) - [Consistency Flow Matching: Defining Straight Flows with Velocity Consistency](https://mlsanity.com/paper/2407.02398/) (2024) - [PeRFlow: Piecewise Rectified Flow as Universal Plug-and-Play Accelerator](https://mlsanity.com/paper/2405.07510/) (2024) - [One-Step Flow Policy Mirror Descent](https://mlsanity.com/paper/2507.23675/) (2025) - [CMT: Mid-Training for Efficient Learning of Consistency, Mean Flow, and Flow Map Models](https://mlsanity.com/paper/2509.24526/) (2025) - [Local Flow Matching Generative Models](https://mlsanity.com/paper/2410.02548/) (2024) - [Toward Theoretical Insights into Diffusion Trajectory Distillation via Operator Merging](https://mlsanity.com/paper/2505.16024/) (2025) - [Analyzing the Feature Extractor Networks for Face Image Synthesis](https://mlsanity.com/paper/2406.02153/) (2024) - [Block Flow: Learning Straight Flow on Data Blocks](https://mlsanity.com/paper/2501.11361/) (2025) - [CAT-Flow: Curvature-Adaptive sTeps for Flow Matching](https://mlsanity.com/paper/2609.01746/) (2026) - [Model-Aware Schedules Improve Generation via Fiberwise Optimal Transport](https://mlsanity.com/paper/2609.11842/) (2026) ## Abstract (arXiv) Flow matching is a powerful framework for generating high-quality samples in various applications, especially image synthesis. However, the intensive computational demands of these models, especially during the finetuning process and sampling processes, pose significant challenges for low-resource scenarios. This paper introduces Bellman Optimal Stepsize Straightening (BOSS) technique for distilling flow-matching generative models: it aims specifically for a few-step efficient image sampling while adhering to a computational budget constraint. First, this technique involves a dynamic programming algorithm that optimizes the stepsizes of the pretrained network. Then, it refines the velocity network to match the optimal step sizes, aiming to straighten the generation paths. Extensive experimental evaluations across image generation tasks demonstrate the efficacy of BOSS in terms of both resource utilization and image quality. Our results reveal that BOSS achieves substantial gains in efficiency while maintaining competitive sample quality, effectively bridging the gap between low-resource constraints and the demanding requirements of flow-matching generative models. Our paper also fortifies the responsible development of artificial intelligence, offering a more sustainable generative model that reduces computational costs and environmental footprints. Our code can be found at https://github.com/nguyenngocbaocmt02/BOSS.