# Diffusion Model for Data-Driven Black-Box Optimization

arXiv: https://arxiv.org/abs/2403.13219 · HTML: https://mlsanity.com/paper/2403.13219/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 77 of its 111 references that are in the map.
- First posted on arXiv 20 Mar 2024.

## Placed in

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

## Builds on (most cited first, 30 of 77)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoisers](https://mlsanity.com/paper/2211.01324/) (2022)
- [Offline Reinforcement Learning as One Big Sequence Modeling Problem](https://mlsanity.com/paper/2106.02039/) (2021)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [MOReL : Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2005.05951/) (2020)
- [Improving alignment of dialogue agents via targeted human judgements](https://mlsanity.com/paper/2209.14375/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)

## Built on by (most cited first, 24 of 24)

- [An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization](https://mlsanity.com/paper/2404.07771/) (2024)
- [Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity](https://mlsanity.com/paper/2405.15986/) (2024)
- [Generative Models in Decision Making: A Survey](https://mlsanity.com/paper/2502.17100/) (2025)
- [Provable Maximum Entropy Manifold Exploration via Diffusion Models](https://mlsanity.com/paper/2506.15385/) (2025)
- [Diffusion Models as Network Optimizers: Explorations and Analysis](https://mlsanity.com/paper/2411.00453/) (2024)
- [Diffusion Models in Simulation-Based Inference: A Tutorial Review](https://mlsanity.com/paper/2512.20685/) (2025)
- [Steering Generative Models with Experimental Data for Protein Fitness Optimization](https://mlsanity.com/paper/2505.15093/) (2025)
- [Verifier-Constrained Flow Expansion for Discovery Beyond the Data](https://mlsanity.com/paper/2602.15984/) (2026)
- [Diffusion Transformer Captures Spatial-Temporal Dependencies: A Theory for Gaussian Process Data](https://mlsanity.com/paper/2407.16134/) (2024)
- [ReGuidance: A Simple Diffusion Wrapper for Boosting Sample Quality on Hard Inverse Problems](https://mlsanity.com/paper/2506.10955/) (2025)
- [Generative Reliability-Based Design Optimization Using In-Context Learning Capabilities of Large Language Models](https://mlsanity.com/paper/2503.22401/) (2025)
- [BaNEL: Exploration Posteriors for Generative Modeling Using Only Negative Rewards](https://mlsanity.com/paper/2510.09596/) (2025)
- [Constrained Flow Optimization via Sequential Fine Tuning for Molecular Design](https://mlsanity.com/paper/2605.30610/) (2026)
- [Adjoint-Based Aerodynamic Shape Optimization with a Manifold Constraint Learned by Diffusion Models](https://mlsanity.com/paper/2507.23443/) (2025)
- [A Reward-Directed Diffusion Framework for Generative Design Optimization](https://mlsanity.com/paper/2508.01509/) (2025)
- [SPREAD: Sampling-based Pareto front Refinement via Efficient Adaptive Diffusion](https://mlsanity.com/paper/2509.21058/) (2025)
- [A Gradient Guided Diffusion Framework for Chance Constrained Programming](https://mlsanity.com/paper/2510.12238/) (2025)
- [On the Robustness of Distribution Support under Diffusion Guidance](https://mlsanity.com/paper/2605.07220/) (2026)
- [Regret Analysis of Guided Diffusion for Black-Box Optimization over Structured Inputs](https://mlsanity.com/paper/2605.10385/) (2026)
- [GOAL: Graph-based Objective-Aligned Diffusion Solvers for Dynamic Multi-Objective Optimization](https://mlsanity.com/paper/2605.19119/) (2026)
- [Multi-Objective Learning for Diffusion Models: A Statistical Theory under Semi-Supervised Learning](https://mlsanity.com/paper/2605.25210/) (2026)
- [Improving Bayesian Optimization via Training-Aware Conditional Diffusion Models](https://mlsanity.com/paper/2606.08438/) (2026)
- [Spec2Twin-Chain: Orchestrating Bi-Level Optimization with LLMs for Blockchain Digital Twin Construction](https://mlsanity.com/paper/2608.30050/) (2026)
- [D-IMPL: A Diffusion-based Solver for Parameterized BBOs](https://mlsanity.com/paper/2609.22752/) (2026)

## Abstract (arXiv)

Generative AI has redefined artificial intelligence, enabling the creation of innovative content and customized solutions that drive business practices into a new era of efficiency and creativity. In this paper, we focus on diffusion models, a powerful generative AI technology, and investigate their potential for black-box optimization over complex structured variables. Consider the practical scenario where one wants to optimize some structured design in a high-dimensional space, based on massive unlabeled data (representing design variables) and a small labeled dataset. We study two practical types of labels: 1) noisy measurements of a real-valued reward function and 2) human preference based on pairwise comparisons. The goal is to generate new designs that are near-optimal and preserve the designed latent structures. Our proposed method reformulates the design optimization problem into a conditional sampling problem, which allows us to leverage the power of diffusion models for modeling complex distributions. In particular, we propose a reward-directed conditional diffusion model, to be trained on the mixed data, for sampling a near-optimal solution conditioned on high predicted rewards. Theoretically, we establish sub-optimality error bounds for the generated designs. The sub-optimality gap nearly matches the optimal guarantee in off-policy bandits, demonstrating the efficiency of reward-directed diffusion models for black-box optimization. Moreover, when the data admits a low-dimensional latent subspace structure, our model efficiently generates high-fidelity designs that closely respect the latent structure. We provide empirical experiments validating our model in decision-making and content-creation tasks.