George Webber

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.

Recovering true signals from noisy measurements is a central challenge in inverse problems spanning medical imaging, geophysics, and signal processing. Current solutions balance prior assumptions regarding the true signal (regularization) with agreement to noisy measured data (data-fidelity). Conventional data-fidelity loss functions, such as mean-squared error (MSE) or negative log-likelihood, seek pointwise agreement with noisy measurements, often leading to overfitting to noise. In this work, we instead evaluate data-fidelity collectively by testing whether the observed measurements are statistically consistent with the noise distributions implied by the current estimate. We adopt this aggregated perspective and introduce distributional consistency (DC) loss, a data-fidelity objective that replaces pointwise matching with distribution-level calibration using model-based probability scores for each measurement. DC loss acts as a direct and practical plug-in replacement for standard data consistency terms: i) it is compatible with modern regularizers, ii) it is optimized in the same way as traditional losses, and iii) it avoids overfitting to measurement noise even without the use of priors. Its scope naturally fits many practical inverse problems where the measurement-noise distribution is known and where the measured dataset consists of many independent noisy values. We demonstrate efficacy in two key example application areas: i) in image denoising with deep image prior, using DC instead of MSE loss removes the need for early stopping and achieves higher PSNR; ii) in medical image reconstruction from Poisson-noisy data, DC loss reduces artifacts in highly-iterated reconstructions and enhances the efficacy of hand-crafted regularization. These results position DC loss as a statistically grounded, performance-enhancing alternative to conventional fidelity losses for inverse problems.

Medical image reconstruction with pretrained score-based generative models (SGMs) has advantages over other existing state-of-the-art deep-learned reconstruction methods, including improved resilience to different scanner setups and advanced image distribution modeling. SGM-based reconstruction has recently been applied to simulated positron emission tomography (PET) datasets, showing improved contrast recovery for out-of-distribution lesions relative to the state-of-the-art. However, existing methods for SGM-based reconstruction from PET data suffer from slow reconstruction, burdensome hyperparameter tuning and slice inconsistency effects (in 3D). In this work, we propose a practical methodology for fully 3D reconstruction that accelerates reconstruction and reduces the number of critical hyperparameters by matching the likelihood of an SGM’s reverse diffusion process to a current iterate of the maximum-likelihood expectation maximization algorithm. Using the example of low-count reconstruction from simulated [¹⁸F]DPA-714 datasets, we show our methodology can match or improve on the NRMSE and SSIM of existing state-of-the-art SGM-based PET reconstruction while reducing reconstruction time and the need for hyperparameter tuning. We evaluate our methodology against state-of-the-art supervised and conventional reconstruction algorithms. Finally, we demonstrate a first-ever implementation of SGM-based reconstruction for real 3D PET data, specifically [¹⁸F]DPA-714 data, where we integrate perpendicular pre-trained SGMs to eliminate slice inconsistency issues.

Better algorithms for medical image reconstruction can improve image quality and enable reductions in acquisition time and radiation dose. A prior understanding of the distribution of plausible images is key to realising these benefits. Recently, research into deep-learning image reconstruction has started to look into using unsupervised diffusion models, trained only on high-quality medical images (i.e. without needing paired scanner measurement data), for modelling this prior understanding. Image reconstruction algorithms incorporating unsupervised diffusion models have already attained state-of-the-art accuracy for reconstruction tasks ranging from highly accelerated MRI to ultra-sparse-view CT and low-dose PET. Key advantages of diffusion model approach over previous deep learning approaches for reconstruction include state-of-the-art image distribution modelling, improved robustness to domain shift, and principled quantification of reconstruction uncertainty. If hallucination concerns can be alleviated, their key advantages and impressive performance could mean these algorithms are better suited to clinical use than previous deep-learning approaches. In this review, we provide an accessible introduction to image reconstruction and diffusion models, outline guidance for using diffusion-model-based reconstruction methodology, summarise modality-specific challenges, and identify key research themes. We conclude with a discussion of the opportunities and challenges of using diffusion models for medical image reconstruction.