A unified perspective on fine-tuning and sampling with diffusion and flow models

• URL: http://arxiv.org/abs/2605.00229v1
• Date: Thu, 30 Apr 2026 21:06:46 GMT
• Title: A unified perspective on fine-tuning and sampling with diffusion and flow models
• Abstract summary: We study the problem of training diffusion and flow generative models to sample from target densities defined by an exponential tilting of a base density.<n>This problem can be approached from an optimal control (SOC) perspective, using adjoint-based or score matching methods, or from a non-equilibrium thermodynamics perspective.
• Score: 22.218023926601106
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the problem of training diffusion and flow generative models to sample from target distributions defined by an exponential tilting of a base density; a formulation that subsumes both sampling from unnormalized densities and reward fine-tuning of pre-trained models. This problem can be approached from a stochastic optimal control (SOC) perspective, using adjoint-based or score matching methods, or from a non-equilibrium thermodynamics perspective. We provide a unified framework encompassing these approaches and make three main contributions: (i) bias-variance decompositions revealing that Adjoint Matching/Sampling and Novel Score Matching have finite gradient variance, while Target and Conditional Score Matching do not; (ii) norm bounds on the lean adjoint ODE that theoretically support the effectiveness of adjoint-based methods; and (iii) adaptations of the CMCD and NETS loss functions, along with novel Crooks and Jarzynski identities, to the exponential tilting setting. We validate our analysis with reward fine-tuning experiments on Stable Diffusion 1.5 and 3.

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