Error-Corrected Inference-Time Scaling for Imperfect Diffusion Models

2026-10-01

AI Summary

This study addresses the issue that inference-time scaling methods inherit errors from imperfections in pretrained diffusion models. To overcome this, we propose an energy-based Feynman–Kac corrector. By deriving continuous-time Feynman–Kac dynamics to eliminate model bias and integrating sequential Monte Carlo with variational guidance techniques for variance control, our method ensures precise sampling through online correction of mismatches between path tracking and the terminal distribution. Experiments across diverse molecular systems demonstrate that the proposed approach significantly reduces sampling errors while accurately matching target distributions and free energy landscapes. This work establishes a new paradigm for reliable generation with diffusion models.

Abstract

Inference-time scaling adapts pretrained diffusion models to new sampling tasks without additional training. Existing methods rely primarily on Monte Carlo sampling with more particles, yet are premised on the pretrained model being exact. In practice, data and training limitations make the model imperfect, and these methods inherit its error. More particles reduce Monte Carlo error but cannot remove the mismatch between the endpoint and the desired target or the error in tracking the prescribed probability path. We introduce the Energy-based Feynman-Kac Corrector (EBFKC), a framework for energy-based diffusion models that corrects these errors on the fly given a reference energy. We first derive Feynman-Kac dynamics that track a prescribed path exactly in the continuous-time population limit even when the model is imperfect, and approximate these dynamics using sequential Monte Carlo with variance-controlling guidance. To remove the endpoint mismatch, we use the pretrained energy as a surrogate along the diffusion path and progressively incorporate the discrepancy between the learned and target terminal energies. Experiments on Gaussian mixture models, particle systems, alanine dipeptide, and alanine tetrapeptide show that our method closely matches target distributions and molecular free-energy profiles under annealing and reward tilting, whereas standard inference-time scaling baselines retain substantial sampling errors.

Problem

• Diffusion Models
• Inference-Time Scaling
• Imperfect Models
• Endpoint Mismatch
• Sampling Error

Innovation

• Inference-time scaling
• Feynman-Kac dynamics
• Energy-based diffusion models
• Sequential Monte Carlo
• Error correction