Efficient Adjoint Matching for Fine-tuning Diffusion Models

TL;DR

This paper introduces Efficient Adjoint Matching (EAM), a novel method that significantly accelerates reward fine-tuning of diffusion models by reformulating the optimal control problem, achieving up to 4x faster convergence while maintaining or improving performance.

Contribution

EAM reformulates the SOC problem with a linear base drift and modified terminal cost, removing inefficiencies and enabling faster, deterministic training without backward adjoint simulation.

Findings

EAM converges up to 4x faster than Adjoint Matching.

EAM matches or surpasses AM in various reward metrics.

EAM maintains high-quality text-to-image generation performance.

Abstract

Reward fine-tuning has become a common approach for aligning pretrained diffusion and flow models with human preferences in text-to-image generation. Among reward-gradient-based methods, Adjoint Matching (AM) provides a principled formulation by casting reward fine-tuning as a stochastic optimal control (SOC) problem. However, AM inevitably requires a substantial computational cost: it requires (i) stochastic simulation of full generative trajectories under memoryless dynamics, resulting in a large number of function evaluations, and (ii) backward ODE simulation of the adjoint state along each sampled trajectory. In this work, we observe that both bottlenecks are closely tied to the \textit{non-trivial base drift} inherited from the pretrained model. Motivated by this observation, we propose \textbf{Efficient Adjoint Matching (EAM)}, which substantially improves training efficiency by reformulating the SOC problem with a \textit{linear base drift} and a correspondingly modified \textit{terminal cost}. This reformulation removes both sources of inefficiency; it enables training-time sampling with a few-step deterministic ODE solver and yields a closed-form adjoint solution that eliminates backward adjoint simulation. On standard text-to-image reward fine-tuning benchmarks, EAM converges up to 4x faster than AM and matches or surpasses it across various metrics including PickScore, ImageReward, HPSv2.1, CLIPScore and Aesthetics.