Steepest Guidance: A Practical and Principled Approach to Inference-Time Alignment of Flow and Diffusion-based Models

2026-09-30

AI Summary

This study addresses the challenge of estimating the optimal guidance via the Doob h-transform for inference alignment in flow and diffusion models. To this end, it proposes the Steepest Guidance framework, which abandons conventional h-transform estimation and reformulates inference alignment as a sequential optimization problem over probability measure spaces. This work pioneers a novel sequential optimization paradigm based on maximizing local improvements, achieving efficient guidance through local gradient ascent. Furthermore, the authors establish a comprehensive theoretical analysis framework that provides rigorous guarantees for the proposed method. Extensive experiments validate both the effectiveness and practical utility of the approach, demonstrating its potential to facilitate robust inference alignment in generative modeling without relying on intractable h-transform approximations.

Abstract

Inference-time alignment of flow and diffusion-based models is critical for achieving flexible generative modeling. Theoretically, Doob's $h$-transform provides an elegant solution to this problem, and most existing methods are based on this principle. However, in practice, estimating the optimal guidance derived from Doob's $h$-transform at inference time is challenging. To deal with this issue, we regard inference-time alignment as a sequential optimization problem in the space of probability measures and propose a novel framework called *Steepest Guidance*, based on the principle of maximizing local improvement in the objective. We provide a theoretical analysis of the proposed method and demonstrate its effectiveness through extensive experiments.

Problem

• inference-time alignment
• flow models
• diffusion models
• Doob's h-transform
• generative modeling

Innovation

• Inference-time alignment
• Steepest Guidance
• Flow and diffusion models
• Sequential optimization
• Probability measures