Training-Free Adaptation of Diffusion Models via Doob's $h$-Transform

We propose D-DOIT (Discrete Doob-Oriented Inference-time Transformation), a training-free and efficient adaptation method for discrete diffusion models with generic rewards. D-DOIT formulates adaptation as sampling from a reward-tilted target distribution and realizes this transport through Doob's h-transform of the discrete diffusion reverse kernel, using only reward values rather than reward gradients. Unlike continuous diffusion, masked discrete diffusion samples categorical token-reveal transitions rather than continuous state updates. D-DOIT derives the corresponding discrete Doob's h-transform, which guides sampling by reweighting reverse transition probabilities instead of adding a drift correction. To make this transformation practical, D-DOIT avoids expensive future rollouts. At each guided step, D-DOIT samples candidate next states, uses the model prediction head to complete each candidate into a clean sequence, evaluates each completion with the reward oracle, and resamples the next state with probabilities proportional to the rewards. An optional late-stage best-of-K refinement further improves sample quality by branching trajectories only near the end of denoising, avoiding the $K$-fold cost over the full trajectory. Empirically, across regulatory DNA design and protein inverse folding benchmarks, D-DOIT outperforms training-free guidance baselines. It improves enhancer activity and cell-type specificity while preserving sequence naturalness, and achieves the highest success rate in protein inverse folding.

Reward-based diffusion fine-tuning faces practical challenges when desirable outcomes are rare or conditioning corrections are costly to estimate. In this work, we propose Diffusion Online $h$-guidance Fine-tuning (DOHF), which turns Doob's $h$-transform into a practical online training algorithm. DOHF assigns optimality weights to generated samples, estimates the normalized local correction $\nabla\log h$ under the current rollout policy, and distills it directly into the generative model. Theoretically, we characterize the population-optimal DiffusionNFT update as well as the various classfier free guidance methods through a unified $h$-transform perspective. Methodologically, our framework accommodates black-box and non-differentiable rewards without additional network evaluations. We further show improved alignments under three empirical scenarios. Our work demonstrates how adapting probabilistic conditioning through inexpensive estimation and iterative distillation can improve generative learning across statistical sampling and visual generation.

Fine-tuning large diffusion models for new domains or styles involves a trade-off: improving target-specific generation often degrades the pretrained model's broad generative capability. Existing full and parameter-efficient fine-tuning methods typically handle this trade-off only implicitly. In this work, we propose a novel source-prior-driven selective adaptation method to efficiently fine-tune diffusion models, achieving a favorable trade-off. Our method relies on two key observations: (1) the loss of general generative capability is highly inconsistent across pretrained parameters, and (2) parameters that have a relatively small impact on the model's general generative capability remain structurally inconsistent across layers and parameter types. Motivated by these observations, we first learn a static mask to explicitly identify parameters better suited for downstream adaptation, and then construct structured update strategies for the selected subset. Experiments show that our method achieves a better adaptation-retention trade-off than existing strong baselines.