dorsal/arxiv
View SchemaInference-Time Alignment for Diffusion Models via Doob's Matching
| Authors | Jinyuan Chang, Chenguang Duan, Yuling Jiao, Yi Xu, Jerry Zhijian Yang |
|---|---|
| Categories | |
| ArXiv ID | 2601.06514vv1 |
| URL | https://arxiv.org/abs/2601.06514 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
Inference-time alignment for diffusion models aims to adapt a pre-trained diffusion model toward a target distribution without retraining the base score network, thereby preserving the generative capacity of the base model while enforcing desired properties at the inference time. A central mechanism for achieving such alignment is guidance, which modifies the sampling dynamics through an additional drift term. In this work, we introduce Doob's matching, a novel framework for guidance estimation grounded in Doob's $h$-transform. Our approach formulates guidance as the gradient of logarithm of an underlying Doob's $h$-function and employs gradient-penalized regression to simultaneously estimate both the $h$-function and its gradient, resulting in a consistent estimator of the guidance. Theoretically, we establish non-asymptotic convergence rates for the estimated guidance. Moreover, we analyze the resulting controllable diffusion processes and prove non-asymptotic convergence guarantees for the generated distributions in the 2-Wasserstein distance.
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"abstract": "Inference-time alignment for diffusion models aims to adapt a pre-trained diffusion model toward a target distribution without retraining the base score network, thereby preserving the generative capacity of the base model while enforcing desired properties at the inference time. A central mechanism for achieving such alignment is guidance, which modifies the sampling dynamics through an additional drift term. In this work, we introduce Doob\u0027s matching, a novel framework for guidance estimation grounded in Doob\u0027s $h$-transform. Our approach formulates guidance as the gradient of logarithm of an underlying Doob\u0027s $h$-function and employs gradient-penalized regression to simultaneously estimate both the $h$-function and its gradient, resulting in a consistent estimator of the guidance. Theoretically, we establish non-asymptotic convergence rates for the estimated guidance. Moreover, we analyze the resulting controllable diffusion processes and prove non-asymptotic convergence guarantees for the generated distributions in the 2-Wasserstein distance.",
"arxiv_id": "2601.06514",
"authors": [
"Jinyuan Chang",
"Chenguang Duan",
"Yuling Jiao",
"Yi Xu",
"Jerry Zhijian Yang"
],
"categories": [
"stat.ML",
"cs.LG",
"cs.NA",
"math.NA",
"math.OC",
"math.ST",
"stat.TH"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Inference-Time Alignment for Diffusion Models via Doob\u0027s Matching",
"url": "https://arxiv.org/abs/2601.06514",
"version": "v1"
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