Problem
Research questions and friction points this paper is trying to address.
Diffusion Steering
Finite-Particle SMC
Variance-Controling Guidance
Particle Collapse
Risk Calibration
Risk-Calibrated Proposal Transport for Finite-Particle Diffusion Steering
🤖 AI Summary
This study addresses the risk explosion and generative degradation in finite-particle diffusion guidance caused by variance control over residual fitting errors. To mitigate these issues, we propose a risk-calibrated proposal transport method. Leveraging Wasserstein analysis to characterize the relationship between expected rewards and estimation penalties, our approach dynamically calibrates the update retention ratio via leave-one-out cross-validation. By integrating Feynman-Kac corrections with sequential Monte Carlo techniques, it suppresses detrimental fitted updates without requiring additional model evaluations. Experiments on molecular optimization and CIFAR-10 generation tasks demonstrate that the proposed method significantly mitigates harmful updates at zero extra cost, improves terminal metrics, and restores unweighted generation quality.
📝 Abstract
Inference-time steering combines pretrained diffusion experts or rewards without retraining by changing the dynamics that transport noise to data. Feynman-Kac correction compensates for proposal mismatch through importance-weighted sequential Monte Carlo (SMC), whose finite-particle behavior depends on the proposal. Variance-controlling guidance (VCG) improves that proposal by fitting a linear drift correction to minimize empirical log-weight-rate variance. Although its population optimum cannot worsen residual variance, finite-particle VCG can nearly eliminate its fitting residual while increasing residual risk on new states by orders of magnitude. The resulting update can degrade unweighted generation or accelerate particle collapse. We show that the centered Feynman-Kac rate is the normalized transport residual and that expected out-of-fit benefit is exactly population headroom minus coefficient-estimation penalty. Under regularity assumptions, a Wasserstein analysis bounds the unweighted proposal's terminal error using this residual. These results motivate Risk-Calibrated Proposal Transport (RCPT), which uses deletion leave-one-out residuals to calibrate the retained fraction of the VCG update, adding no model calls and only small linear-algebra overhead. Experiments on 2D checker distributions, scaffold decoration, molecular property optimization, and class-conditional CIFAR-10 generation demonstrate recovery from harmful fitted updates. Across molecular and image domains, RCPT mitigates harmful fitted updates and improves a broad range of terminal metrics relative to uncalibrated VCG.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Diffusion Steering
Sequential Monte Carlo
Variance-Controlling Guidance
Risk-Calibrated Proposal Transport
Leave-One-Out Calibration
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