Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priors

2025-10-12

AI Summary

For Bayesian inverse problems where derivatives of the forward model are inaccessible, this paper proposes BLADE: the first method to integrate diffusion models as data-driven priors into derivative-free inversion frameworks, enabling compatibility with black-box forward models. BLADE employs an interacting particle system for gradient-free posterior sampling and is supported by non-asymptotic convergence theory, ensuring both posterior accuracy and calibration. Compared to existing derivative-free approaches, BLADE achieves substantial improvements in parameter recovery accuracy and posterior uncertainty quantification across diverse inverse problems—including highly nonlinear fluid dynamics—demonstrating robust performance under complex scientific computing scenarios. By unifying expressive prior modeling, derivative-free inference, and rigorous theoretical guarantees, BLADE establishes a new paradigm for efficient, reliable, and provably sound Bayesian inference.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Derivative-free Bayesian inversion is an important task in many science and engineering applications, particularly when computing the forward model derivative is computationally and practically challenging. In this paper, we introduce Blade, which can produce accurate and well-calibrated posteriors for Bayesian inversion using an ensemble of interacting particles. Blade leverages powerful data-driven priors based on diffusion models, and can handle nonlinear forward models that permit only black-box access (i.e., derivative-free). Theoretically, we establish a non-asymptotic convergence analysis to characterize the effects of forward model and prior estimation errors. Empirically, Blade achieves superior performance compared to existing derivative-free Bayesian inversion methods on various inverse problems, including challenging highly nonlinear fluid dynamics.

Problem

• Solving derivative-free Bayesian inversion with diffusion priors
• Handling nonlinear forward models via black-box access
• Analyzing convergence with forward model estimation errors

Innovation

• Derivative-free Bayesian inversion using diffusion priors
• Ensemble of interacting particles for accurate posteriors
• Handles nonlinear forward models with black-box access