# Gradual Fine-Tuning for Flow Matching Models

arXiv: https://arxiv.org/abs/2601.22495 · HTML: https://mlsanity.com/paper/2601.22495/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 38 of its 52 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## 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, 30 of 38)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [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)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [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)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Directly Fine-Tuning Diffusion Models on Differentiable Rewards](https://mlsanity.com/paper/2309.17400/) (2023)
- [Functional Map of the World](https://mlsanity.com/paper/1711.07846/) (2017)
- [Aligning Text-to-Image Diffusion Models with Reward Backpropagation](https://mlsanity.com/paper/2310.03739/) (2023)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Control](https://mlsanity.com/paper/2402.15194/) (2024)
- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)
- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [Dirichlet Flow Matching with Applications to DNA Sequence Design](https://mlsanity.com/paper/2402.05841/) (2024)
- [AlphaFold Meets Flow Matching for Generating Protein Ensembles](https://mlsanity.com/paper/2402.04845/) (2024)
- [How to build a consistency model: Learning flow maps via self-distillation](https://mlsanity.com/paper/2505.18825/) (2025)
- [ReinFlow: Fine-tuning Flow Matching Policy with Online Reinforcement Learning](https://mlsanity.com/paper/2505.22094/) (2025)
- [Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matching](https://mlsanity.com/paper/2504.11713/) (2025)
- [Aesthetic Post-Training Diffusion Models from Generic Preferences with Step-by-step Preference Optimization](https://mlsanity.com/paper/2406.04314/) (2024)
- [Simulation-free Schr"odinger bridges via score and flow matching](https://mlsanity.com/paper/2307.03672/) (2023)
- [Fisher Flow Matching for Generative Modeling over Discrete Data](https://mlsanity.com/paper/2405.14664/) (2024)
- [RxRx1: A Dataset for Evaluating Experimental Batch Correction Methods](https://mlsanity.com/paper/2301.05768/) (2023)

## Abstract (arXiv)

Fine-tuning flow matching models is a central challenge in settings with limited data, evolving distributions, or computational constraints. While recent work has produced significant advances, particularly in the area of reward-based fine-tuning, current methods fail to demonstrate both theoretical correctness as well as strong empirical results in terms of stability, efficiency, and diversity preservation. In this work, we propose Gradual Fine-Tuning (GFT), a simple yet principled annealing-based framework for fine-tuning flow generative models when only samples from the target distribution are available. For stochastic flows, GFT defines a temperature-controlled sequence of intermediate objectives that smoothly interpolate between the pretrained and target drifts, provably approaching the true target as the temperature approaches zero. We analytically demonstrate that sample generation after GFT can be made substantially more efficient with the use of arbitrary (e.g., optimal transport) couplings, as well as by utilizing few-step inference methods. Empirically, GFT significantly improves convergence stability, while maintaining or improving generation quality, training speed, and generation diversity compared to other fine-tuning methods. Our results position GFT as a simple yet theoretically grounded and practically effective alternative for scalable adaptation of flow matching models under distribution shift.