# Diffusion Models for Black-Box Optimization

arXiv: https://arxiv.org/abs/2306.07180 · HTML: https://mlsanity.com/paper/2306.07180/

## Key facts

- Cited by 76 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 39 of its 50 references that are in the map.
- First posted on arXiv 12 Jun 2023.

## Placed in

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

## Builds on (most cited first, 30 of 39)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Gotta Go Fast When Generating Data with Score-Based Models](https://mlsanity.com/paper/2105.14080/) (2021)
- [Online Decision Transformer](https://mlsanity.com/paper/2202.05607/) (2022)
- [A Variational Perspective on Diffusion-Based Generative Models and Score Matching](https://mlsanity.com/paper/2106.02808/) (2021)
- [Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling](https://mlsanity.com/paper/1802.09127/) (2018)
- [Diff-TTS: A Denoising Diffusion Model for Text-to-Speech](https://mlsanity.com/paper/2104.01409/) (2021)
- [Transformer Neural Processes: Uncertainty-Aware Meta Learning Via Sequence Modeling](https://mlsanity.com/paper/2207.04179/) (2022)
- [Conditioning by adaptive sampling for robust design](https://mlsanity.com/paper/1901.10060/) (2019)
- [Design-Bench: Benchmarks for Data-Driven Offline Model-Based Optimization](https://mlsanity.com/paper/2202.08450/) (2022)
- [Blurring Diffusion Models](https://mlsanity.com/paper/2209.05557/) (2022)
- [Leaving Reality to Imagination: Robust Classification via Generated Datasets](https://mlsanity.com/paper/2302.02503/) (2023)
- [Conservative Objective Models for Effective Offline Model-Based Optimization](https://mlsanity.com/paper/2107.06882/) (2021)
- [Guided-TTS: A Diffusion Model for Text-to-Speech via Classifier Guidance](https://mlsanity.com/paper/2111.11755/) (2021)
- [Model Inversion Networks for Model-Based Optimization](https://mlsanity.com/paper/1912.13464/) (2019)
- [Autofocused oracles for model-based design](https://mlsanity.com/paper/2006.08052/) (2020)

## Built on by (most cited first, 30 of 76)

- [Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Review](https://mlsanity.com/paper/2407.13734/) (2024)
- [An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization](https://mlsanity.com/paper/2404.07771/) (2024)
- [Enhancing Deep Reinforcement Learning: A Tutorial on Generative Diffusion Models in Network Optimization](https://mlsanity.com/paper/2308.05384/) (2023)
- [Feedback Efficient Online Fine-Tuning of Diffusion Models](https://mlsanity.com/paper/2402.16359/) (2024)
- [Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints](https://mlsanity.com/paper/2402.18012/) (2024)
- [Diamond Maps: Efficient Reward Alignment via Stochastic Flow Maps](https://mlsanity.com/paper/2602.05993/) (2026)
- [LICO: Large Language Models for In-Context Molecular Optimization](https://mlsanity.com/paper/2406.18851/) (2024)
- [Bridging Model-Based Optimization and Generative Modeling via Conservative Fine-Tuning of Diffusion Models](https://mlsanity.com/paper/2405.19673/) (2024)
- [Diffusion Model for Data-Driven Black-Box Optimization](https://mlsanity.com/paper/2403.13219/) (2024)
- [ExPT: Synthetic Pretraining for Few-Shot Experimental Design](https://mlsanity.com/paper/2310.19961/) (2023)
- [GTA: Generative Trajectory Augmentation with Guidance for Offline Reinforcement Learning](https://mlsanity.com/paper/2405.16907/) (2024)
- [DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization](https://mlsanity.com/paper/2403.05571/) (2024)
- [Diffusion Models are Evolutionary Algorithms](https://mlsanity.com/paper/2410.02543/) (2024)
- [GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Models](https://mlsanity.com/paper/2509.25170/) (2025)
- [Guided Trajectory Generation with Diffusion Models for Offline Model-based Optimization](https://mlsanity.com/paper/2407.01624/) (2024)
- [Generative Models in Decision Making: A Survey](https://mlsanity.com/paper/2502.17100/) (2025)
- [Offline Model-Based Optimization: Comprehensive Review](https://mlsanity.com/paper/2503.17286/) (2025)
- [Offline Multi-Objective Optimization](https://mlsanity.com/paper/2406.03722/) (2024)
- [Pretrained Optimization Model for Zero-Shot Black Box Optimization](https://mlsanity.com/paper/2405.03728/) (2024)
- [Offline Model-Based Optimization by Learning to Rank](https://mlsanity.com/paper/2410.11502/) (2024)
- [Diffusion Models as Network Optimizers: Explorations and Analysis](https://mlsanity.com/paper/2411.00453/) (2024)
- [Posterior Inference with Diffusion Models for High-dimensional Black-box Optimization](https://mlsanity.com/paper/2502.16824/) (2025)
- [Preference-Guided Diffusion for Multi-Objective Offline Optimization](https://mlsanity.com/paper/2503.17299/) (2025)
- [Constraint-Aware Diffusion Models for Trajectory Optimization](https://mlsanity.com/paper/2406.00990/) (2024)
- [Generative Adversarial Model-Based Optimization via Source Critic Regularization](https://mlsanity.com/paper/2402.06532/) (2024)
- [Expensive Multi-Objective Bayesian Optimization Based on Diffusion Models](https://mlsanity.com/paper/2405.08674/) (2024)
- [Design Editing for Offline Model-based Optimization](https://mlsanity.com/paper/2405.13964/) (2024)
- ["Noisier" Noise Contrastive Eestimation is (Almost) Maximum Likelihood](https://mlsanity.com/paper/2405.16730/) (2024)
- [Robust Guided Diffusion for Offline Black-Box Optimization](https://mlsanity.com/paper/2410.00983/) (2024)
- [Fast Direct: Query-Efficient Online Black-box Guidance for Diffusion-model Target Generation](https://mlsanity.com/paper/2502.01692/) (2025)

## Abstract (arXiv)

The goal of offline black-box optimization (BBO) is to optimize an expensive black-box function using a fixed dataset of function evaluations. Prior works consider forward approaches that learn surrogates to the black-box function and inverse approaches that directly map function values to corresponding points in the input domain of the black-box function. These approaches are limited by the quality of the offline dataset and the difficulty in learning one-to-many mappings in high dimensions, respectively. We propose Denoising Diffusion Optimization Models (DDOM), a new inverse approach for offline black-box optimization based on diffusion models. Given an offline dataset, DDOM learns a conditional generative model over the domain of the black-box function conditioned on the function values. We investigate several design choices in DDOM, such as re-weighting the dataset to focus on high function values and the use of classifier-free guidance at test-time to enable generalization to function values that can even exceed the dataset maxima. Empirically, we conduct experiments on the Design-Bench benchmark and show that DDOM achieves results competitive with state-of-the-art baselines.