# Risk-Calibrated Proposal Transport for Finite-Particle Diffusion Steering

arXiv: https://arxiv.org/abs/2610.04171 · HTML: https://mlsanity.com/paper/2610.04171/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 51 references that are in the map.
- First posted on arXiv 3 Oct 2026.

## Builds on (most cited first, 29 of 29)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [FreeDoM: Training-Free Energy-Guided Conditional Diffusion Model](https://mlsanity.com/paper/2303.09833/) (2023)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Models](https://mlsanity.com/paper/2406.08070/) (2024)
- [TFG: Unified Training-Free Guidance for Diffusion Models](https://mlsanity.com/paper/2409.15761/) (2024)
- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Equivariant Energy-Guided SDE for Inverse Molecular Design](https://mlsanity.com/paper/2209.15408/) (2022)
- [Particle Denoising Diffusion Sampler](https://mlsanity.com/paper/2402.06320/) (2024)
- [Elements of Sequential Monte Carlo](https://mlsanity.com/paper/1903.04797/) (2019)
- [Denoising Likelihood Score Matching for Conditional Score-based Data Generation](https://mlsanity.com/paper/2203.14206/) (2022)
- [Diffusion Tree Sampling: Scalable inference-time alignment of diffusion models](https://mlsanity.com/paper/2506.20701/) (2025)
- [Debiasing Guidance for Discrete Diffusion with Sequential Monte Carlo](https://mlsanity.com/paper/2502.06079/) (2025)
- [DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Models](https://mlsanity.com/paper/2509.21655/) (2025)
- [Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlo](https://mlsanity.com/paper/2502.12786/) (2025)
- [Mechanisms of Projective Composition of Diffusion Models](https://mlsanity.com/paper/2502.04549/) (2025)
- [Inference-Time Scaling of Discrete Diffusion Models via Importance Weighting and Optimal Proposal Design](https://mlsanity.com/paper/2505.22524/) (2025)
- [Regularized Zero-Variance Control Variates](https://mlsanity.com/paper/1811.05073/) (2018)
- [Discrete Feynman-Kac Correctors](https://mlsanity.com/paper/2601.10403/) (2026)
- [Tuning Sequential Monte Carlo Samplers via Greedy Incremental Divergence Minimization](https://mlsanity.com/paper/2503.15704/) (2025)
- [Inference-Time Alignment of Diffusion Models via Trust-Region Iterative Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2605.25123/) (2026)
- [On the Collapse of Generative Paths: A Criterion and Correction for Diffusion Steering](https://mlsanity.com/paper/2512.10339/) (2025)
- [VGAS: Variance-Reduced Guidance and Adaptive Selection for Training-Free Reward Alignment in Discrete Diffusion](https://mlsanity.com/paper/2608.26585/) (2026)

## Abstract (arXiv)

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.