{
  "abstract": "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.",
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  "arxiv": "2610.20035",
  "author_total": 2,
  "authors": [
    {
      "name": "Eliot Beyler"
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    {
      "name": "Francis Bach"
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  "bibtex": "https://research.draconitic.com/paper/b5e7c1bwn32tz.bib",
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  "doi": "10.48550/arxiv.2610.20035",
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  "pdf_url": "https://hal.science/hal-05795740/document",
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  "published": "2026-10-12",
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  "ris": "https://research.draconitic.com/paper/b5e7c1bwn32tz.ris",
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      "url": "https://arxiv.org/abs/2610.20035"
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  "subjects": [
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      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
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  "title": "Weighted Adjoint Matching: Finetuning Flow Matching Models with Time-Dependent Control Cost",
  "title_text": "Weighted Adjoint Matching: Finetuning Flow Matching Models with Time-Dependent Control Cost",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/b5e7c1bwn32tz",
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