Spectra: Exact Component Transport for Test-Time Prior Adaptation in Simulation-Based Inference

2026-10-06

AI Summary

This study addresses the challenge of adapting pretrained diffusion models to test-time prior distribution shifts in simulation-based inference. To this end, it proposes Spectra, a method that introduces the first closed-form solution based on an exact score transport identity. Spectra enables instantaneous adaptation to structured prior shifts without requiring retraining or additional simulations. Evaluated across six benchmarks, the proposed approach achieves accurate inference under strong prior shifts with minimal online sampling costs, effectively overcoming the computational bottlenecks of conventional methods. These results validate both the theoretical superiority and practical efficacy of the underlying framework.

Abstract

Simulation-based inference (SBI) has become a powerful approach to Bayesian inference in complex scientific models whose likelihoods are difficult or impossible to evaluate. Amortized SBI learns reusable inference models from simulated data, enabling rapid posterior inference for new observations, and modern generative models have made these models increasingly expressive. However, this reuse is limited to the prior distribution chosen during training, whereas scientific analyses often need revised priors as knowledge accumulates or alternative assumptions are tested. We introduce Spectra, a test-time adaptation method for diffusion-based SBI. Spectra uses an exact score-transport identity to obtain the adapted score from a frozen diffusion model in closed form for structured prior changes, without additional simulation or training. Across six SBI benchmarks, Spectra achieves accurate adaptation under strong prior shifts at low online sampling cost. This enables pretrained SBI models to incorporate updated prior information at test time.

Problem

• Simulation-based inference
• Amortized inference
• Prior adaptation
• Test-time adaptation
• Bayesian inference

Innovation

• Simulation-Based Inference
• Test-Time Adaptation
• Diffusion Models
• Score Transport
• Prior Adaptation