# Distributional Multi-objective Black-box Optimization for Diffusion-model Inference-time Multi-Target Generation

arXiv: https://arxiv.org/abs/2510.26278 · HTML: https://mlsanity.com/paper/2510.26278/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 7 of its 26 references that are in the map.
- First posted on arXiv 30 Oct 2025.

## Placed in

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

## Builds on (most cited first, 7 of 7)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [GuacaMol: Benchmarking Models for De Novo Molecular Design](https://mlsanity.com/paper/1811.09621/) (2018)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [Surrogate Assisted Evolutionary Algorithm for Medium Scale Expensive Multi-Objective Optimisation Problems](https://mlsanity.com/paper/2002.03150/) (2020)

## Abstract (arXiv)

Diffusion models have been successful in learning complex data distributions. This capability has driven their application to high-dimensional multi-objective black-box optimization problem. Existing approaches often employ an external optimization loop, such as an evolutionary algorithm, to the diffusion model. However, these approaches treat the diffusion model as a black-box refiner, which overlooks the internal distribution transition of the diffusion generation process, limiting their efficiency. To address these challenges, we propose the Inference-time Multi-target Generation (IMG) algorithm, which optimizes the diffusion process at inference-time to generate samples that simultaneously satisfy multiple objectives. Specifically, our IMG performs weighted resampling during the diffusion generation process according to the expected aggregated multi-objective values. This weighted resampling strategy ensures the diffusion-generated samples are distributed according to our desired multi-target Boltzmann distribution. We further derive that the multi-target Boltzmann distribution has an interesting log-likelihood interpretation, where it is the optimal solution to the distributional multi-objective optimization problem. We implemented IMG for a multi-objective molecule generation task. Experiments show that IMG, requiring only a single generation pass, achieves a significantly higher hypervolume than baseline optimization algorithms that often require hundreds of diffusion generations. Notably, our algorithm can be viewed as an optimized diffusion process and can be integrated into existing methods to further improve their performance.