# Bayesian Experimental Design via Contrastive Diffusions

arXiv: https://arxiv.org/abs/2410.11826 · HTML: https://mlsanity.com/paper/2410.11826/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 63 references that are in the map.
- First posted on arXiv 15 Oct 2024.

## Builds on (most cited first, 30 of 34)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Critic](https://mlsanity.com/paper/2007.05170/) (2020)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019)
- [Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design](https://mlsanity.com/paper/2103.02438/) (2021)
- [Provably Faster Algorithms for Bilevel Optimization](https://mlsanity.com/paper/2106.04692/) (2021)
- [A framework for bilevel optimization that enables stochastic and global variance reduction algorithms](https://mlsanity.com/paper/2201.13409/) (2022)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [Implicit Deep Adaptive Design: Policy-Based Experimental Design without Likelihoods](https://mlsanity.com/paper/2111.02329/) (2021)
- [A Unified Stochastic Gradient Approach to Designing Bayesian-Optimal Experiments](https://mlsanity.com/paper/1911.00294/) (2019)
- [Optimizing Sequential Experimental Design with Deep Reinforcement Learning](https://mlsanity.com/paper/2202.00821/) (2022)
- [Optimal experimental design: Formulations and computations](https://mlsanity.com/paper/2407.16212/) (2024)
- [Deep Learning-based Image and Video Inpainting: A Survey](https://mlsanity.com/paper/2401.03395/) (2024)
- [Variance reduction properties of the reparameterization trick](https://mlsanity.com/paper/1809.10330/) (2018)
- [Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Data](https://mlsanity.com/paper/2305.01166/) (2023)
- [A Guide Through the Zoo of Biased SGD](https://mlsanity.com/paper/2305.16296/) (2023)
- [Gradient-based Bayesian Experimental Design for Implicit Models using Mutual Information Lower Bounds](https://mlsanity.com/paper/2105.04379/) (2021)
- [Implicit Diffusion: Efficient Optimization through Stochastic Sampling](https://mlsanity.com/paper/2402.05468/) (2024)
- [Sequential Bayesian Experimental Design for Implicit Models via Mutual Information](https://mlsanity.com/paper/2003.09379/) (2020)
- [Diffusive Gibbs Sampling](https://mlsanity.com/paper/2402.03008/) (2024)
- [Unbiased MLMC stochastic gradient-based optimization of Bayesian experimental designs](https://mlsanity.com/paper/2005.08414/) (2020)
- [Nesting Particle Filters for Experimental Design in Dynamical Systems](https://mlsanity.com/paper/2402.07868/) (2024)
- [Conditioning diffusion models by explicit forward-backward bridging](https://mlsanity.com/paper/2405.13794/) (2024)

## Built on by (most cited first, 11 of 11)

- [Step-DAD: Semi-Amortized Policy-Based Bayesian Experimental Design](https://mlsanity.com/paper/2507.14057/) (2025)
- [Foundation Models for Scientific Discovery: From Paradigm Enhancement to Paradigm Transition](https://mlsanity.com/paper/2510.15280/) (2025)
- [JADAI: Jointly Amortizing Adaptive Design and Bayesian Inference](https://mlsanity.com/paper/2512.22999/) (2025)
- [A Geometric Approach to Optimal Experimental Design](https://mlsanity.com/paper/2510.14848/) (2025)
- [Action-BED: Task-Driven Bayesian Experimental Design with Singly Intractable Objectives](https://mlsanity.com/paper/2606.23662/) (2026)
- [When Are Two Scores Better Than One? Investigating Ensembles of Diffusion Models](https://mlsanity.com/paper/2601.11444/) (2026)
- [Active MRI Acquisition with Diffusion Guided Bayesian Experimental Design](https://mlsanity.com/paper/2506.16237/) (2025)
- [Bayesian experimental design: grouped geometric pooled posterior via ensemble Kalman methods](https://mlsanity.com/paper/2604.18505/) (2026)
- [Goal-driven Bayesian Optimal Experimental Design for Robust Decision-Making Under Model Uncertainty](https://mlsanity.com/paper/2605.26093/) (2026)
- [FairBED: A Bayesian Experimental Design Approach to Gathering Fairer Data](https://mlsanity.com/paper/2606.23515/) (2026)
- [GPARA: Graph-Posterior-Aligned Refinement and Active Acquisition for Grounding Diffusion Priors](https://mlsanity.com/paper/2609.34172/) (2026)

## Abstract (arXiv)

Bayesian Optimal Experimental Design (BOED) is a powerful tool to reduce the cost of running a sequence of experiments. When based on the Expected Information Gain (EIG), design optimization corresponds to the maximization of some intractable expected contrast between prior and posterior distributions. Scaling this maximization to high dimensional and complex settings has been an issue due to BOED inherent computational complexity. In this work, we introduce a pooled posterior distribution with cost-effective sampling properties and provide a tractable access to the EIG contrast maximization via a new EIG gradient expression. Diffusion-based samplers are used to compute the dynamics of the pooled posterior and ideas from bi-level optimization are leveraged to derive an efficient joint sampling-optimization loop. The resulting efficiency gain allows to extend BOED to the well-tested generative capabilities of diffusion models. By incorporating generative models into the BOED framework, we expand its scope and its use in scenarios that were previously impractical. Numerical experiments and comparison with state-of-the-art methods show the potential of the approach.