Solving Inverse Problems with Flow-based Models via Model Predictive Control

George Webber, Alexander Denker, Riccardo Barbano, Andrew J. Reader
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:133377-133402, 2026.

Abstract

Flow-based generative models provide strong unconditional priors for inverse problems, but guiding their dynamics for conditional generation remains challenging. Recent work casts training-free conditional generation in flow models as an optimal control problem; however, solving the resulting trajectory optimisation is computationally and memory intensive, requiring differentiation through the flow dynamics or adjoint solves. We propose MPC-Flow, a model predictive control framework that formulates inverse problem solving with flow-based generative models as a sequence of control sub-problems, enabling practical optimal control-based guidance at inference time. We provide theoretical analysis linking MPC-Flow to the underlying optimal control objective and show how different algorithmic choices yield a spectrum of guidance algorithms, including regimes that avoid backpropagation through the generative model trajectory. We evaluate MPC-Flow on benchmark image restoration tasks, spanning linear and non-linear settings such as in-painting, deblurring, and super-resolution, and demonstrate strong performance and scalability to massive state-of-the-art architectures via training-free guidance of FLUX.2 (32B) in a quantised setting on consumer hardware.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-webber26a, title = {Solving Inverse Problems with Flow-based Models via Model Predictive Control}, author = {Webber, George and Denker, Alexander and Barbano, Riccardo and Reader, Andrew J.}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {133377--133402}, 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/webber26a/webber26a.pdf}, url = {https://proceedings.mlr.press/v306/webber26a.html}, abstract = {Flow-based generative models provide strong unconditional priors for inverse problems, but guiding their dynamics for conditional generation remains challenging. Recent work casts training-free conditional generation in flow models as an optimal control problem; however, solving the resulting trajectory optimisation is computationally and memory intensive, requiring differentiation through the flow dynamics or adjoint solves. We propose MPC-Flow, a model predictive control framework that formulates inverse problem solving with flow-based generative models as a sequence of control sub-problems, enabling practical optimal control-based guidance at inference time. We provide theoretical analysis linking MPC-Flow to the underlying optimal control objective and show how different algorithmic choices yield a spectrum of guidance algorithms, including regimes that avoid backpropagation through the generative model trajectory. We evaluate MPC-Flow on benchmark image restoration tasks, spanning linear and non-linear settings such as in-painting, deblurring, and super-resolution, and demonstrate strong performance and scalability to massive state-of-the-art architectures via training-free guidance of FLUX.2 (32B) in a quantised setting on consumer hardware.} }
Endnote
%0 Conference Paper %T Solving Inverse Problems with Flow-based Models via Model Predictive Control %A George Webber %A Alexander Denker %A Riccardo Barbano %A Andrew J. Reader %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-webber26a %I PMLR %P 133377--133402 %U https://proceedings.mlr.press/v306/webber26a.html %V 306 %X Flow-based generative models provide strong unconditional priors for inverse problems, but guiding their dynamics for conditional generation remains challenging. Recent work casts training-free conditional generation in flow models as an optimal control problem; however, solving the resulting trajectory optimisation is computationally and memory intensive, requiring differentiation through the flow dynamics or adjoint solves. We propose MPC-Flow, a model predictive control framework that formulates inverse problem solving with flow-based generative models as a sequence of control sub-problems, enabling practical optimal control-based guidance at inference time. We provide theoretical analysis linking MPC-Flow to the underlying optimal control objective and show how different algorithmic choices yield a spectrum of guidance algorithms, including regimes that avoid backpropagation through the generative model trajectory. We evaluate MPC-Flow on benchmark image restoration tasks, spanning linear and non-linear settings such as in-painting, deblurring, and super-resolution, and demonstrate strong performance and scalability to massive state-of-the-art architectures via training-free guidance of FLUX.2 (32B) in a quantised setting on consumer hardware.
APA
Webber, G., Denker, A., Barbano, R. & Reader, A.J.. (2026). Solving Inverse Problems with Flow-based Models via Model Predictive Control. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:133377-133402 Available from https://proceedings.mlr.press/v306/webber26a.html.

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