Regret Analysis of Guided Diffusion for Black-Box Optimization over Structured Inputs

Authors: Masaki Adachi, Anita Yang, Yakun Wang et al.

arXiv · PDF

Summary

The authors develop a regret analysis framework for using pretrained diffusion models in black-box optimization over structured inputs like molecules or crystals. Traditional Bayesian optimization regret bounds rely on maximum information gain and exact acquisition maximization, which don't apply when you're using a pretrained diffusion model as a structural prior and sampling candidates rather than exactly optimizing an acquisition function. They propose a certificate-based framework where the key quantity is "mass lift" — how much more probability the guided diffusion assigns to near-optimal designs compared to the pretrained generator.

Main takeaways:

• Existing Bayesian optimization regret analyses don't apply to guided-diffusion pipelines because they assume non-pretrained surrogates and exact acquisition maximization.
• The authors introduce a certificate-based expected simple-regret framework that avoids maximum-information-gain bounds and RKHS assumptions.
• The central quantity is "mass lift": the increase in probability mass assigned to near-optimal designs relative to the pretrained generator.
• This view explains how exponential-looking finite-budget convergence and polynomial acceleration can arise from the same mechanism.
• The paper provides practical diagnostics for estimating search exponents from finite candidate pools and a proposal-corrected resampling construction for certified sampling.

Relevance

Not related to my LLM persona work — this is about black-box optimization over structured chemical/material designs using diffusion models. No connection to behavioral installation, prompt equivalence, or activation steering in language models.

Abstract

arXiv:2605.10385v1 Announce Type: new Abstract: Guided-diffusion black-box optimization (BO) has shown strong empirical performance on structured design problems such as molecules and crystals, but its regret behavior remains poorly understood. Existing BO regret analyses typically rely on maximum information gain, non-pretrained surrogate models, or exact acquisition maximization -- assumptions that break down in modern diffusion -- BO pipelines, where pretrained diffusion models serve as powerful priors over valid structures and acquisition maximization is replaced by approximate sampling over astronomically large discrete spaces. We develop a first certificate-based expected simple-regret framework for guided-diffusion BO that avoids maximum-information-gain bounds, RKHS assumptions, and exact acquisition maximization. The central quantity in our analysis is mass lift: the increase in probability mass assigned to near-optimal designs relative to the pretrained generator. This view explains how exponential-looking finite-budget convergence and polynomial acceleration can all arise from the same mechanism. We also give practical diagnostics for estimating search exponents from finite candidate pools and a proposal-corrected resampling construction that provides a fully certified sampler instance.