Exact Conditional Score-Guided Generative Modeling for Amortized Inference in Uncertainty Quantification

2025-06-22

AI Summary

Efficient conditional sampling from high-dimensional, multimodal posterior distributions remains challenging in uncertainty quantification. Method: We propose a non-iterative, non-invertible generative modeling framework. Leveraging the analytically tractable conditional score function under a Gaussian mixture prior, we construct a training-free diffusion model; a feedforward neural network directly predicts the denoising direction, bypassing invertibility constraints of normalizing flows and iterative solvers of conventional diffusion models. Sampling is achieved via a single forward pass using backward ordinary differential equation (ODE) integration and noise-label supervision. Contribution/Results: Experiments demonstrate that our method achieves state-of-the-art accuracy while significantly accelerating sampling—by multiple times over existing approaches—making it particularly suitable for real-world uncertainty quantification tasks such as parameter estimation in complex physical systems.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Computer Vision: Diffusion Models for Vision

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We propose an efficient framework for amortized conditional inference by leveraging exact conditional score-guided diffusion models to train a non-reversible neural network as a conditional generative model. Traditional normalizing flow methods require reversible architectures, which can limit their expressiveness and efficiency. Although diffusion models offer greater flexibility, they often suffer from high computational costs during inference. To combine the strengths of both approaches, we introduce a two-stage method. First, we construct a training-free conditional diffusion model by analytically deriving an exact score function under a Gaussian mixture prior formed from samples of the underlying joint distribution. This exact conditional score model allows us to efficiently generate noise-labeled data, consisting of initial diffusion Gaussian noise and posterior samples conditioned on various observation values, by solving a reverse-time ordinary differential equation. Second, we use this noise-labeled data to train a feedforward neural network that maps noise and observations directly to posterior samples, eliminating the need for reversibility or iterative sampling at inference time. The resulting model provides fast, accurate, and scalable conditional sampling for high-dimensional and multi-modal posterior distributions, making it well-suited for uncertainty quantification tasks, e.g., parameter estimation of complex physical systems. We demonstrate the effectiveness of our approach through a series of numerical experiments.

Problem

• Efficient amortized conditional inference using exact score-guided diffusion models
• Overcoming limitations of reversible architectures in normalizing flow methods
• Fast scalable sampling for high-dimensional multi-modal posterior distributions

Innovation

• Exact conditional score-guided diffusion models
• Two-stage non-reversible neural training
• Fast feedforward posterior sampling