Sampling via Stochastic Interpolants by Langevin-based Velocity and Initialization Estimation in Flow ODEs
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910048336216064 |
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| author | Duan, Chenguang Jiao, Yuling Steidl, Gabriele Wald, Christian Yang, Jerry Zhijian Zhang, Ruizhe |
| author_facet | Duan, Chenguang Jiao, Yuling Steidl, Gabriele Wald, Christian Yang, Jerry Zhijian Zhang, Ruizhe |
| contents | We propose a novel method for sampling from unnormalized Boltzmann densities based on a probability flow ordinary differential equation (ODE) derived from linear stochastic interpolants. The key innovation of our approach is the use of a sequence of Langevin samplers to enable efficient simulation of the flow. Specifically, these Langevin samplers are employed (i) to generate samples from the interpolant distribution at intermediate times and (ii) to construct, starting from these intermediate times, a robust estimator of the velocity field governing the probability flow ODE. Theoretically, we provide convergence guarantees for both Langevin components, and establish a non-asymptotic convergence rate for the probability flow ODE. Extensive numerical experiments demonstrate the efficiency of the proposed method on challenging multimodal distributions across a range of dimensions, as well as its effectiveness in Bayesian inference tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08527 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sampling via Stochastic Interpolants by Langevin-based Velocity and Initialization Estimation in Flow ODEs Duan, Chenguang Jiao, Yuling Steidl, Gabriele Wald, Christian Yang, Jerry Zhijian Zhang, Ruizhe Numerical Analysis Machine Learning Probability We propose a novel method for sampling from unnormalized Boltzmann densities based on a probability flow ordinary differential equation (ODE) derived from linear stochastic interpolants. The key innovation of our approach is the use of a sequence of Langevin samplers to enable efficient simulation of the flow. Specifically, these Langevin samplers are employed (i) to generate samples from the interpolant distribution at intermediate times and (ii) to construct, starting from these intermediate times, a robust estimator of the velocity field governing the probability flow ODE. Theoretically, we provide convergence guarantees for both Langevin components, and establish a non-asymptotic convergence rate for the probability flow ODE. Extensive numerical experiments demonstrate the efficiency of the proposed method on challenging multimodal distributions across a range of dimensions, as well as its effectiveness in Bayesian inference tasks. |
| title | Sampling via Stochastic Interpolants by Langevin-based Velocity and Initialization Estimation in Flow ODEs |
| topic | Numerical Analysis Machine Learning Probability |
| url | https://arxiv.org/abs/2601.08527 |