mlsanityData to 14 Oct 2026

Weighted Adjoint Matching: Finetuning Flow Matching Models with Time-Dependent Control Cost

arXiv 2610.20035 ↗First posted 14 Oct 2026stat.ML cs.LGcited by 0

On the map: Diffusion models → Flow matching, time series and science also fits: Diffusion and flow policies for robotics

Abstract (arXiv)

We introduce Weighted Adjoint Matching, a method to finetune a pretrained diffusion or flow matching model given a differentiable reward. We derive it from Adjoint Matching, which reformulates finetuning as a stochastic optimal control problem with a quadratic control cost. Building on the observation that these models generate coarse features before fine details, we place a time-dependent weight on the control cost. A high cost early in the generative process preserves balance and diversity in the coarse features, which carry most of the semantics, while a low cost at the end lets the model increase the reward by refining details. We prove that our method is equivalent to maximizing the reward under time-varying Kullback--Leibler regularization on the generative paths. Experiments on Gaussian mixtures and on MNIST show a better tradeoff between reward and mode balance than Adjoint Matching.

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 35 of its 46 references that are in the map. First posted on arXiv 14 Oct 2026.

Builds on

35 of 46 references.

Closest ancestors · 3

Same direction, newest first

  1. 2025Tilt Matching for Scalable Sampling and Fine-Tuning26 Dec
  2. 2022Flow Matching for Generative Modeling6 Oct
  3. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 32

  1. 2020Denoising Diffusion Implicit Modelscited by 9,781
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  5. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  6. 2023ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generationcited by 1,045
  7. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  8. 2023Training Diffusion Models with Reinforcement Learningcited by 982
  9. 2023DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Modelscited by 450
  10. 2023Directly Fine-Tuning Diffusion Models on Differentiable Rewardscited by 448
  11. 2017Certifying Some Distributional Robustness with Principled Adversarial Trainingcited by 337
  12. 2024Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Controlcited by 233
20 more
  1. 2016Distributionally Robust Stochastic Optimization with Wasserstein Distancecited by 185
  2. 2022Generative Modelling With Inverse Heat Dissipationcited by 167
  3. 2024Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Controlcited by 143
  4. 2024Dynamical Regimes of Diffusion Modelscited by 142
  5. 2024Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Reviewcited by 98
  6. 2025TempFlow-GRPO: When Timing Matters for GRPO in Flow Modelscited by 97
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  8. 2023Spontaneous Symmetry Breaking in Generative Diffusion Modelscited by 80
  9. 2023Diffusion Models Generate Images Like Painters: an Analytical Theory of Outline First, Details Latercited by 55
  10. 2024Critical windows: non-asymptotic theory for feature emergence in diffusion modelscited by 47
  11. 2023Stochastic Optimal Control Matchingcited by 40
  12. 2024Implicit Diffusion: Efficient Optimization through Stochastic Samplingcited by 24
  13. 2024Stochastic Control for Fine-tuning Diffusion Models: Optimality, Regularity, and Convergencecited by 19
  14. 2025DiverseGRPO: Mitigating Mode Collapse in Image Generation via Diversity-Aware GRPOcited by 17
  15. 2024Avoiding mode collapse in diffusion models fine-tuned with reinforcement learningcited by 12
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  17. 2026Adjoint Matching through the Lens of the Stochastic Maximum Principle in Optimal Controlcited by 6
  18. 2026Improved techniques for fine-tuning flow models via adjoint matching: a deterministic control pipelinecited by 5
  19. 2026Differentiating through Stochastic Differential Equations: A Primercited by 2
  20. 2026The tractability landscape of diffusion alignment: regularization, rewards, and computational primitivescited by 2

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