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

• URL: http://arxiv.org/abs/2601.23231v1
• Date: Fri, 30 Jan 2026 17:59:09 GMT
• Title: Solving Inverse Problems with Flow-based Models via Model Predictive Control
• Authors: George Webber, Alexander Denker, Riccardo Barbano, Andrew J Reader,
• Abstract summary: MPC-Flow is a model predictive control framework that formulates inverse problem solving with flow-based generative models as a sequence of control sub-problems.<n>We show how different algorithmic choices yield a spectrum of guidance algorithms, including regimes that avoid backpropagation through the generative model trajectory.
• Score: 41.551726534223704
• License: http://creativecommons.org/licenses/by/4.0/
• 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 guarantees 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.

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