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Bayesian Experimental Design Via Contrastive Diffusions

ICLR 2025 · Probabilistic and scientific modeling › Uncertainty and Gaussian processes · approach: Simulation-based inference

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Introduces CoDiff, a single-loop gradient-based BOED method using a pooled posterior and diffusion-based samplers to maximize expected information gain, enabling data-based BOED with generative priors.

Problem

Expected information gain (EIG) maximization for Bayesian optimal experimental design is doubly intractable and computationally expensive in high-dimensional and sequential settings, and prior work could not handle priors available only through samples.

Approach

Derives a new EIG gradient expression using a pooled posterior (logarithmic pooling of posteriors over sampled outcomes) as importance proposal, and couples sampling and design optimization in a single bi-level loop, with diffusion models supplying conditional samplers for data-based priors.

Key results

• On source localization, CoDiff improves SPCE by about 30% over the non-myopic RL-BOED baseline and yields Wasserstein distances about two orders of magnitude lower.
• On MNIST image reconstruction, CoDiff reaches SSIM 0.826 after 6 experiments versus 0.463 for random designs.
• Source localization experiments were repeated over 100 random rollouts with N+M=400 samples; each measurement step takes 2.9 s.

Measured effects reported in the paper

Surprising findings

• Greedy (myopic) design via CoDiff outperforms the long-sighted reinforcement learning procedure RL-BOED on the density-based source localization task.

Limitations

• Greedy approach; not non-myopic.
• Requires explicit likelihood expression.
• Diffusion-based inverse problem handling limited to linear forward models.

Experimental setup

Datasets: MNIST

Benchmarks: source localization (sequential BOED, 30 experiments) MNIST image reconstruction from 7x7 masks

Metrics: SPCE SNMC L2 Wasserstein distance SSIM

Baselines: RL-BOED VPCE PASOA SMC Random design

Builds on: implicit diffusion diffusive Gibbs sampling sampling-as-optimization Donsker-Varadhan variational formula score-based inverse problem solvers (FPS)

Closest papers by meaning

• On Estimating the Gradient of the Expected Information Gain in Bayesian Experimental Design (AAAI 2024 · similarity 0.90)
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• Bayesian Adaptive Calibration and Optimal Design (NeurIPS 2024 · similarity 0.87)
• Informed Initialization for Bayesian Optimization and Active Learning (NeurIPS 2025 · similarity 0.87)
• PASOA- PArticle baSed Bayesian Optimal Adaptive design (ICML 2024 · similarity 0.87)
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