SIMANF: Sample Free Learning of Unnormalized Distributions via Simulated Annealing in Normalizing Flows
Abstract
Efficiently learning and sampling from high dimensional, multimodal unnormalized distributions without target samples remains a challenging problem. Although normalizing flows can generate samples efficiently, training based on the reverse KL divergence using only the unnormalized target density may suffer from mode collapse. We introduce SIMANF, a sample free framework that integrates simulated annealing with normalizing flows. SIMANF progressively transforms the target distribution from a smooth initial form to the original target distribution and trains the flow sequentially across these stages. By transferring the learned representation between stages, the method promotes mode coverage while progressively capturing finer features of the target distribution. Following annealing, a final refinement stage combines the reverse KL divergence with an importance weighted forward KL objective using samples generated by the flow. SIMANF requires no target samples during training and uses only the unnormalized density. We demonstrate its effectiveness on Many-Well distributions and high dimensional Scalar Phi4 lattice field theory distribution.
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BibTeX
@misc{kanaujia2026simanf,
title = {{SIMANF: Sample Free Learning of Unnormalized Distributions via Simulated Annealing in Normalizing Flows}},
author = {Vikas Kanaujia},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32279},
eprint = {2609.32279},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32279},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - SIMANF: Sample Free Learning of Unnormalized Distributions via Simulated Annealing in Normalizing Flows
AU - Vikas Kanaujia
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32279
UR - https://arxiv.org/abs/2609.32279
AB - Efficiently learning and sampling from high dimensional, multimodal unnormalized distributions without target samples remains a challenging problem. Although normalizing flows can generate samples efficiently, training based on the reverse KL divergence using only the unnormalized target density may suffer from mode collapse. We introduce SIMANF, a sample free framework that integrates simulated annealing with normalizing flows. SIMANF progressively transforms the target distribution from a smooth initial form to the original target distribution and trains the flow sequentially across these stages. By transferring the learned representation between stages, the method promotes mode coverage while progressively capturing finer features of the target distribution. Following annealing, a final refinement stage combines the reverse KL divergence with an importance weighted forward KL objective using samples generated by the flow. SIMANF requires no target samples during training and uses only the unnormalized density. We demonstrate its effectiveness on Many-Well distributions and high dimensional Scalar Phi4 lattice field theory distribution.
ER -