# Posterior Inference with Diffusion Models for High-dimensional Black-box Optimization

arXiv: https://arxiv.org/abs/2502.16824 · HTML: https://mlsanity.com/paper/2502.16824/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 49 of its 72 references that are in the map.
- First posted on arXiv 24 Feb 2025.

## Placed in

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

## Builds on (most cited first, 30 of 49)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Bayesian Optimization is Superior to Random Search for Machine Learning Hyperparameter Tuning: Analysis of the Black-Box Optimization Challenge 2020](https://mlsanity.com/paper/2104.10201/) (2021)
- [Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Control](https://mlsanity.com/paper/2402.15194/) (2024)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [Sample-Efficient Optimization in the Latent Space of Deep Generative Models via Weighted Retraining](https://mlsanity.com/paper/2006.09191/) (2020)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [Iterated Denoising Energy Matching for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2402.06121/) (2024)
- [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)

## Built on by (most cited first, 13 of 13)

- [Offline Model-Based Optimization: Comprehensive Review](https://mlsanity.com/paper/2503.17286/) (2025)
- [Simplifying Bayesian Optimization Via In-Context Direct Optimum Sampling](https://mlsanity.com/paper/2505.23913/) (2025)
- [Posterior Inference in Latent Space for Scalable Constrained Black-box Optimization](https://mlsanity.com/paper/2507.00480/) (2025)
- [Generative Bayesian Optimization: Generative Models as Acquisition Functions](https://mlsanity.com/paper/2510.25240/) (2025)
- [Task-free Adaptive Meta Black-box Optimization](https://mlsanity.com/paper/2601.21475/) (2026)
- [Regret Analysis of Guided Diffusion for Black-Box Optimization over Structured Inputs](https://mlsanity.com/paper/2605.10385/) (2026)
- [Diverse and Adaptable Arm Coordination for Octopus-Crawling via Diffusion-Based Uncertainty-Aware Optimization](https://mlsanity.com/paper/2609.21138/) (2026)
- [Sample-Efficient Optimisation over the Outputs of Generative Models](https://mlsanity.com/paper/2509.23800/) (2025)
- [Is Sequence Information All You Need for Bayesian Optimization of Antibodies?](https://mlsanity.com/paper/2509.24933/) (2025)
- [StAD: Stein Amortized Divergence for Fast Likelihoods with Diffusion and Flow](https://mlsanity.com/paper/2605.16486/) (2026)
- [Improving Bayesian Optimization via Training-Aware Conditional Diffusion Models](https://mlsanity.com/paper/2606.08438/) (2026)
- [Generative Refinement for Low-Budget Black-Box Optimization](https://mlsanity.com/paper/2607.00691/) (2026)
- [In-Context Batch Black-box Optimization via Flow Matching](https://mlsanity.com/paper/2610.20138/) (2026)

## Abstract (arXiv)

Optimizing high-dimensional and complex black-box functions is crucial in numerous scientific applications. While Bayesian optimization (BO) is a powerful method for sample-efficient optimization, it struggles with the curse of dimensionality and scaling to thousands of evaluations. Recently, leveraging generative models to solve black-box optimization problems has emerged as a promising framework. However, those methods often underperform compared to BO methods due to limited expressivity and difficulty of uncertainty estimation in high-dimensional spaces. To overcome these issues, we introduce DiBO, a novel framework for solving high-dimensional black-box optimization problems. Our method iterates two stages. First, we train a diffusion model to capture the data distribution and deep ensembles to predict function values with uncertainty quantification. Second, we cast the candidate selection as a posterior inference problem to balance exploration and exploitation in high-dimensional spaces. Concretely, we fine-tune diffusion models to amortize posterior inference. Extensive experiments demonstrate that our method outperforms state-of-the-art baselines across synthetic and real-world tasks. Our code is publicly available hrefhttps://github.com/umkiyoung/DiBOhere.