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

Key points

• We derive it from Adjoint Matching, which reformulates finetuning as a stochastic optimal control problem with a quadratic control cost.1
• Building on the observation that these models generate coarse features before fine details, we place a time-dependent weight on the control cost.1
• We prove that our method is equivalent to maximizing the reward under time-varying Kullback--Leibler regularization on the generative paths.1
• Experiments on Gaussian mixtures and on MNIST show a better tradeoff between reward and mode balance than Adjoint Matching.1

Sources (1)

• [1]Weighted Adjoint Matching: Finetuning Flow Matching Models with Time-Dependent Control Cost
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 14, 11:43 AM

  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.

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