Test-Time Guidance for Flow-Based Generative Models via Parallel Tempering on Source Distributions

Shih-Hsin Wang, Joel Keller, Taos Transue, Drake Benjamin Brown, Thomas Strohmer, Bao Wang
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:127427-127449, 2026.

Abstract

Generative models that transport a simple source distribution to a complex data distribution—such as diffusion and flow-based models—are central to high-fidelity data generation. Test-time guidance can further steer pretrained models toward user-specified high-reward regions without costly retraining. However, existing guidance methods face critical limitations: they struggle with non-differentiable rewards, fail to navigate complex landscapes, and often lack theoretical guarantees on generation performance. We propose Source Parallel Tempering (SPT), a gradient-free test-time guidance framework that operates entirely in source space, leveraging its simpler geometry to avoid the complexities of the data manifold. SPT couples a local exploration kernel with parallel tempering, enabling efficient barrier crossing and robust discovery of high-reward modes. Theoretically, we provide a new error bound linking training-time approximation error to test-time guidance performance. Empirically, SPT significantly improves over state-of-the-art methods on benchmark tasks in conditional image synthesis and dynamical system trajectory sampling. Code is available at https://github.com/Utah-Math-Data-Science/SPT.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-wang26da, title = {Test-Time Guidance for Flow-Based Generative Models via Parallel Tempering on Source Distributions}, author = {Wang, Shih-Hsin and Keller, Joel and Transue, Taos and Brown, Drake Benjamin and Strohmer, Thomas and Wang, Bao}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {127427--127449}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/wang26da/wang26da.pdf}, url = {https://proceedings.mlr.press/v306/wang26da.html}, abstract = {Generative models that transport a simple source distribution to a complex data distribution—such as diffusion and flow-based models—are central to high-fidelity data generation. Test-time guidance can further steer pretrained models toward user-specified high-reward regions without costly retraining. However, existing guidance methods face critical limitations: they struggle with non-differentiable rewards, fail to navigate complex landscapes, and often lack theoretical guarantees on generation performance. We propose Source Parallel Tempering (SPT), a gradient-free test-time guidance framework that operates entirely in source space, leveraging its simpler geometry to avoid the complexities of the data manifold. SPT couples a local exploration kernel with parallel tempering, enabling efficient barrier crossing and robust discovery of high-reward modes. Theoretically, we provide a new error bound linking training-time approximation error to test-time guidance performance. Empirically, SPT significantly improves over state-of-the-art methods on benchmark tasks in conditional image synthesis and dynamical system trajectory sampling. Code is available at https://github.com/Utah-Math-Data-Science/SPT.} }
Endnote
%0 Conference Paper %T Test-Time Guidance for Flow-Based Generative Models via Parallel Tempering on Source Distributions %A Shih-Hsin Wang %A Joel Keller %A Taos Transue %A Drake Benjamin Brown %A Thomas Strohmer %A Bao Wang %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-wang26da %I PMLR %P 127427--127449 %U https://proceedings.mlr.press/v306/wang26da.html %V 306 %X Generative models that transport a simple source distribution to a complex data distribution—such as diffusion and flow-based models—are central to high-fidelity data generation. Test-time guidance can further steer pretrained models toward user-specified high-reward regions without costly retraining. However, existing guidance methods face critical limitations: they struggle with non-differentiable rewards, fail to navigate complex landscapes, and often lack theoretical guarantees on generation performance. We propose Source Parallel Tempering (SPT), a gradient-free test-time guidance framework that operates entirely in source space, leveraging its simpler geometry to avoid the complexities of the data manifold. SPT couples a local exploration kernel with parallel tempering, enabling efficient barrier crossing and robust discovery of high-reward modes. Theoretically, we provide a new error bound linking training-time approximation error to test-time guidance performance. Empirically, SPT significantly improves over state-of-the-art methods on benchmark tasks in conditional image synthesis and dynamical system trajectory sampling. Code is available at https://github.com/Utah-Math-Data-Science/SPT.
APA
Wang, S., Keller, J., Transue, T., Brown, D.B., Strohmer, T. & Wang, B.. (2026). Test-Time Guidance for Flow-Based Generative Models via Parallel Tempering on Source Distributions. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:127427-127449 Available from https://proceedings.mlr.press/v306/wang26da.html.

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