VASR: Variance-Aware Systematic Resampling for Reward-Guided Diffusion

Reward-guided discrete diffusion enables test-time alignment with downstream objectives, but applying Sequential Monte Carlo (SMC) guidance at every denoising step is computationally expensive. Active guidance steps require additional reward evaluations and, for gradient-based proposals, value-gradient computations. Sparse guidance reduces this cost by guiding only a subset of timesteps, but commonly used schedules are fixed heuristics whose effectiveness can vary substantially across tasks. We propose VISTA, a training-free method that automatically selects guided timesteps under a fixed budget. VISTA formulates sparse guidance as approximation of the ideal full-guidance probability path and derives an estimable upper bound on $\ell_1$ path deviation. Using value statistics collected from a small number of full-guidance warmup generations, VISTA optimizes the resulting empirical surrogate exactly via dynamic programming. The warmup generations can be retained as model outputs, and after schedule selection VISTA has the same per-generation guidance complexity as other sparse schedules with the same budget. Across text, biological sequence, and image generation tasks, VISTA discovers task-dependent schedules and outperforms hand-designed sparse schedules in most tested settings, while approaching or exceeding full-guidance performance on several task metrics. In toxic-text generation, for example, VISTA attains a 0.99 unique-toxic ratio compared with 1.00 for full guidance while reducing post-selection per-generation latency from 204.23 s to 38.16 s, a 5.35$\times$ speedup.

Masked discrete diffusion models perform strongly on text, code, and biological sequences, but their training objective rewards only naturalness, and retraining the generator for every new reward is expensive. Inference-time steering of a frozen model either guides the sampler by the reward gradient or searches over several trajectories, and recent samplers combine the two. Such combinations are assembled as pipelines that leave three choices at their defaults: a guidance estimate resting on one Gumbel draw per sample, a reward tilting placed without reference to the distribution the combination then targets, and a selection temperature held fixed although the spread of per-step rewards drifts. We identify that distribution and settle the three choices against it. We therefore propose Variance-reduced Guidance and Adaptive Selection (VGAS), a simple yet effective inference-time framework that reduces the variance of the guidance estimate for both reward types, applies the reward tilting in the clean-token logits, where the pretrained schedule is preserved, and sets the selection temperature per step. Across regulatory DNA, protein and small-molecule benchmarks, VGAS attains the best training-free reward and matches or surpasses a reward-fine-tuned generator.

Adapting pretrained diffusion models to downstream objectives such as inverse problems often requires expensive test-time guidance or optimization. We propose a principled framework for generating high-quality reward-aligned samples at substantially reduced inference cost. Our approach formulates test-time adaptation as a hierarchical variational model, where control is amortized into a lightweight yet expressive stochastic policy. This formulation naturally supports few-step diffusion sampling: large step sizes enable fast inference, while the learned policy maintains sample quality by providing structured per-step control. The resulting fully amortized sampler achieves a strong quality--speed tradeoff, matching or exceeding recent test-time scaling baselines while requiring significantly less compute. For example, on 4x super-resolution, our method achieves better perceptual quality with more than 5x faster inference compared to the best-performing baseline. We further extend our approach to a semi-amortized regime that combines cheap amortized proposals with limited test-time optimization, achieving state-of-the-art perceptual quality across several challenging inverse problems.