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

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.

Reward-based fine-tuning steers a pretrained diffusion or flow-based generative model toward higher-reward samples while remaining close to the pretrained model. Although existing methods are derived from different perspectives, we show that many can be written under a common framework, which we call reward score matching (RSM). Under this view, alignment becomes score matching against a value-guided target, and the main differences across methods reduce to the construction of the value-guidance estimator and the effective optimization strength across timesteps. This unification clarifies the bias-variance-compute tradeoffs of existing designs, and distinguishes core optimization components from auxiliary mechanisms that add complexity without clear benefit. Guided by this perspective, we develop simpler, more efficient redesigns across representative differentiable and black-box reward alignment tasks. Overall, RSM turns a seemingly fragmented collection of reward-based fine-tuning methods into a smaller, more interpretable, and more actionable design space. Code is available at https://github.com/jaylee2000/rsm

We propose a deterministic adjoint matching framework that formulates human preference alignment for flow-based generative models as an optimal control problem over velocity fields. One can directly regress the control toward a value-gradient-induced target under the current policy, leading to a simple and stable training objective. Building on this perspective, we introduce a truncated adjoint scheme that focuses computation on the terminal portion of the trajectory, where reward-relevant signals concentrate, which yields substantial computational savings while preserving alignment quality. We further generalize the framework beyond standard KL-based regularization, allowing more flexible trade-offs between alignment strength and distributional preservation. Experiments on SiT-XL/2 and FLUX.2-Klein-4B demonstrate consistent gains across multiple alignment metrics, along with substantially improved diversity and mode preservation.