# Diffusion-BBO: Diffusion-Based Inverse Modeling for Online Black-Box Optimization

arXiv: https://arxiv.org/abs/2407.00610 · HTML: https://mlsanity.com/paper/2407.00610/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- First posted on arXiv 30 Jun 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Built on by (most cited first, 2 of 2)

- [Steering Generative Models with Experimental Data for Protein Fitness Optimization](https://mlsanity.com/paper/2505.15093/) (2025)
- [Generative Refinement for Low-Budget Black-Box Optimization](https://mlsanity.com/paper/2607.00691/) (2026)

## Abstract (arXiv)

Online black-box optimization (BBO) aims to optimize an objective function by iteratively querying a black-box oracle in a sample-efficient way. While prior studies focus on forward approaches such as Gaussian Processes (GPs) to learn a surrogate model for the unknown objective function, they struggle with steering clear of out-of-distribution and invalid designs in scientific discovery tasks. Recently, inverse modeling approaches that map the objective space to the design space with conditional diffusion models have demonstrated impressive capability in learning the data manifold. However, these approaches proceed in an offline fashion with pre-collected data. How to design inverse approaches for online BBO to actively query new data and improve the sample efficiency remains an open question. In this work, we propose Diffusion-BBO, a sample-efficient online BBO framework leveraging the conditional diffusion model as the inverse surrogate model. Diffusion-BBO employs a novel acquisition function Uncertainty-aware Exploration (UaE) to propose scores in the objective space for conditional sampling. We theoretically prove that Diffusion-BBO with UaE achieves a near-optimal solution for online BBO. We also empirically demonstrate that Diffusion-BBO with UaE outperforms existing online BBO baselines across 6 scientific discovery tasks.