Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures

2026-05-19 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

URGE (Unbiased Resampling via Girsanov Estimation) is a novel, derivative-free inference-time scaling algorithm for diffusion models that enhances sample quality on task-specific objectives. Unlike existing guidance techniques that require repeated score or gradient evaluations, URGE performs pathwise importance reweighting using a Girsanov change of measure. It attaches a simple multiplicative weight to each simulated trajectory and periodically resamples, eliminating the need for score, Hessian, or PDE evaluations. The method establishes an equivalence between pathwise and particle-wise Sequential Monte Carlo (SMC), ensuring the same approximation-free terminal law. Empirically, URGE surpasses current inference-time guidance baselines on synthetic tests and diffusion-model benchmarks, delivering superior generation quality with simpler implementation and full gradient-freeness.

Key takeaway

For research scientists developing or deploying diffusion models, URGE offers a robust, approximation-free method to enhance generation quality without the computational burden of gradient-based guidance. You should consider integrating URGE, especially when working with complex or black-box reward functions where derivative computation is impractical or costly, to achieve superior results and simplify implementation.

Key insights

URGE improves diffusion model sample quality via derivative-free pathwise importance reweighting and resampling.

Principles

• Pathwise reweighting offers greater flexibility than particle-space reweighting.
• Girsanov change of measure enables approximation-free bias correction.
• Periodic resampling corrects suboptimal guided generation toward target distributions.

Method

URGE simulates multiple trajectories under guided SDEs, reweights them using a Girsanov path-space likelihood ratio, and periodically resamples based on these weights to correct bias.

In practice

• Apply URGE for improved generation quality in diffusion models.
• Use URGE with black-box reward functions where derivatives are unavailable.
• Discretize time steps finely to ensure stable importance weighting.

Topics

• Diffusion Models
• Inference-Time Guidance
• Sequential Monte Carlo
• Girsanov Estimation
• Pathwise Reweighting

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, AI Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.