NRFlow: Towards Noise-Robust Generative Modeling via High-Order Mechanism

Bo Chen, Chengyue Gong, Xiaoyu Li, Yingyu Liang, Zhizhou Sha, Zhenmei Shi, Zhao Song, Mingda Wan, Xugang Ye
Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, PMLR 286:673-704, 2025.

Abstract

Flow-based generative models have shown promise in various machine learning applications, but they often face challenges in handling noise and ensuring robustness in trajectory estimation. In this work, we propose NRFlow, a novel extension to flow-based generative modeling that incorporates second-order dynamics through acceleration fields. We develop a comprehensive theoretical framework to analyze the regularization effects of high-order terms and derive noise robustness guarantees. Our method leverages a two-part loss function to simultaneously train first-order velocity fields and high-order acceleration fields, enhancing both smoothness and stability in learned transport trajectories. These results highlight the potential of high-order flow matching for robust generative modeling in complex and noisy environments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v286-chen25e, title = {NRFlow: Towards Noise-Robust Generative Modeling via High-Order Mechanism}, author = {Chen, Bo and Gong, Chengyue and Li, Xiaoyu and Liang, Yingyu and Sha, Zhizhou and Shi, Zhenmei and Song, Zhao and Wan, Mingda and Ye, Xugang}, booktitle = {Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence}, pages = {673--704}, year = {2025}, editor = {Chiappa, Silvia and Magliacane, Sara}, volume = {286}, series = {Proceedings of Machine Learning Research}, month = {21--25 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v286/main/assets/chen25e/chen25e.pdf}, url = {https://proceedings.mlr.press/v286/chen25e.html}, abstract = {Flow-based generative models have shown promise in various machine learning applications, but they often face challenges in handling noise and ensuring robustness in trajectory estimation. In this work, we propose NRFlow, a novel extension to flow-based generative modeling that incorporates second-order dynamics through acceleration fields. We develop a comprehensive theoretical framework to analyze the regularization effects of high-order terms and derive noise robustness guarantees. Our method leverages a two-part loss function to simultaneously train first-order velocity fields and high-order acceleration fields, enhancing both smoothness and stability in learned transport trajectories. These results highlight the potential of high-order flow matching for robust generative modeling in complex and noisy environments.} }
Endnote
%0 Conference Paper %T NRFlow: Towards Noise-Robust Generative Modeling via High-Order Mechanism %A Bo Chen %A Chengyue Gong %A Xiaoyu Li %A Yingyu Liang %A Zhizhou Sha %A Zhenmei Shi %A Zhao Song %A Mingda Wan %A Xugang Ye %B Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2025 %E Silvia Chiappa %E Sara Magliacane %F pmlr-v286-chen25e %I PMLR %P 673--704 %U https://proceedings.mlr.press/v286/chen25e.html %V 286 %X Flow-based generative models have shown promise in various machine learning applications, but they often face challenges in handling noise and ensuring robustness in trajectory estimation. In this work, we propose NRFlow, a novel extension to flow-based generative modeling that incorporates second-order dynamics through acceleration fields. We develop a comprehensive theoretical framework to analyze the regularization effects of high-order terms and derive noise robustness guarantees. Our method leverages a two-part loss function to simultaneously train first-order velocity fields and high-order acceleration fields, enhancing both smoothness and stability in learned transport trajectories. These results highlight the potential of high-order flow matching for robust generative modeling in complex and noisy environments.
APA
Chen, B., Gong, C., Li, X., Liang, Y., Sha, Z., Shi, Z., Song, Z., Wan, M. & Ye, X.. (2025). NRFlow: Towards Noise-Robust Generative Modeling via High-Order Mechanism. Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 286:673-704 Available from https://proceedings.mlr.press/v286/chen25e.html.

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