Abstract
We propose a neural algorithm for sampling from distributions specified by unnormalized Boltzmann densities. Our approach is based on the Jordan--Kinderlehrer--Otto scheme for the Kullback--Leibler divergence in the Wasserstein--Fisher--Rao geometry (WFR JKO scheme). Our contributions are twofold. First, we prove that, for any fixed step size, the exact WFR JKO iterates converge exponentially fast to the target as the number of iterations tends to infinity. Notably, this result requires no structural assumptions on the target, such as log-concavity or a logarithmic Sobolev inequality. Second, we develop a neural implementation of the WFR JKO scheme that parametrizes its transport and reaction components using reweighted normalizing flows. Numerical experiments on challenging multimodal targets demonstrate the promising performance of the proposed method.
Keywords
Publication details
- Journal
- Not available
- Open access
- Green open access
Cite this article
APA 7
Duan, C., Hertrich, J., & Steidl, G. (2026). Neural Sampling with Reweighted Normalizing Flows via the Wasserstein--Fisher--Rao JKO Scheme. https://omanscience.com/en/articles/neural-sampling-with-reweighted-normalizing-flows-via-the-wasserstein-fisher-rao-jko-scheme
MLA 9
Duan, Chenguang, et al. "Neural Sampling with Reweighted Normalizing Flows via the Wasserstein--Fisher--Rao JKO Scheme." https://omanscience.com/en/articles/neural-sampling-with-reweighted-normalizing-flows-via-the-wasserstein-fisher-rao-jko-scheme.
Chicago (author–date)
Duan, Chenguang, Johannes Hertrich, and Gabriele Steidl. 2026. "Neural Sampling with Reweighted Normalizing Flows via the Wasserstein--Fisher--Rao JKO Scheme." https://omanscience.com/en/articles/neural-sampling-with-reweighted-normalizing-flows-via-the-wasserstein-fisher-rao-jko-scheme.
Harvard
Duan, C., Hertrich, J. and Steidl, G. (2026) 'Neural Sampling with Reweighted Normalizing Flows via the Wasserstein--Fisher--Rao JKO Scheme', Available at: https://omanscience.com/en/articles/neural-sampling-with-reweighted-normalizing-flows-via-the-wasserstein-fisher-rao-jko-scheme.
Vancouver
Duan C, Hertrich J, Steidl G. Neural Sampling with Reweighted Normalizing Flows via the Wasserstein--Fisher--Rao JKO Scheme. https://omanscience.com/en/articles/neural-sampling-with-reweighted-normalizing-flows-via-the-wasserstein-fisher-rao-jko-scheme
IEEE
C. Duan, J. Hertrich, and G. Steidl, "Neural Sampling with Reweighted Normalizing Flows via the Wasserstein--Fisher--Rao JKO Scheme," https://omanscience.com/en/articles/neural-sampling-with-reweighted-normalizing-flows-via-the-wasserstein-fisher-rao-jko-scheme.