computational imaging engineers

Abstract: Generative models are transforming Bayesian computational imaging, yet the field still lacks physics-aware foundation models. Current practice falls into two camps. Large foundation image models are deployed as plug-and-play priors with zero-shot approximate likelihood guidance, which introduces significant bias and computational cost. Physics-aware generative models avoid this bias, but each is tied to a specific dataset, task and instrument. We introduce BAM (Bayesian Anything Model), a lightweight foundation model for few-step, physics-aware posterior sampling that generalises robustly to unseen data and tasks, zero-shot or with minimal finetuning. BAM upgrades the operator-conditioned Reconstruct Anything Model (RAM) backbone (Terris et al.) into a conditional flow map, so instrument physics is specified at inference time rather than fixed during training. BAM has just 36M parameters and is pre-trained jointly on large image corpora and libraries of forward operators. A single network then draws posterior samples in a few steps, with no likelihood approximation and no guidance weights to tune. Across linear inverse problems on FFHQ, AFHQ, LSUN, DIV2K and the Kohler camera-shake benchmark, BAM outperforms in just 3 steps both specialised models and leading zero-shot methods in sample quality, at a fraction of their computational cost. BAM gives the community an accessible entry point to generative computational imaging, lowers the economic and environmental cost of training imaging models, and opens a new path for research on physics-aware Bayesian computational imaging. Official page: https://bayesian-anything-model.github.io/

Abstract: Coded diffraction patterns (CDPs) provide a structured and physically relevant model for phase retrieval, but the dependence among Fourier measurements generated by a common mask makes sharp stability analysis challenging. For a fixed unit-norm signal $\boldsymbol{x}_\star \in \mathbb{C}^n$, let $\boldsymbol{X}_\star=\boldsymbol{x}_\star\boldsymbol{x}_\star^*$, and let $\mathcal A$ be the lifted CDP measurement operator. We prove that, with $L=O(\log n)$ random masks, the following uniform lower isometry holds with high probability: $\|\boldsymbol{X}-\boldsymbol{X}_\star\|_F \lesssim \log^2(2n) \frac{\|\mathcal A(\boldsymbol{X}-\boldsymbol{X}_\star)\|_2}{\sqrt{nL}}, \boldsymbol{X}\succeq\boldsymbol{0},$ from which we derive two consequences. First, for $\boldsymbol{y}=\mathcal A(\boldsymbol{X}_\star)+\boldsymbol{e}$, PhaseLift-type convex programs achieve the Gaussian-type stable recovery bound $\|\widehat{\boldsymbol{X}}-\boldsymbol{X}_\star\|_F \lesssim \frac{\log^2(2n)}{\sqrt{nL}}\|\boldsymbol{e}\|_2.$ Second, in the noiseless case, the nonconvex factorized loss has a benign landscape when the factor width satisfies $r = O(\log^5(2n))$: every second-order critical point $\boldsymbol{V}\in\mathbb C^{n\times r}$ satisfies $\boldsymbol{V}\boldsymbol{V}^*=\boldsymbol{X}_\star$. The key ingredient is a uniform operator-norm bound over row subsets of the dependent CDP measurement matrix, which permits the removal of a controlled set of adaptively selected rows while preserving tangent injectivity.

Abstract: Split Gibbs sampling enables diffusion posterior inference for general nonlinear inverse problems by decoupling prior and likelihood computations, allowing a pretrained diffusion prior to be reused across measurement models. However, its likelihood update often relies on iterative MCMC, which can hinder parallelization, require algorithm-specific tuning, and incur substantial computational cost. In this work, we propose a learning-based framework to replace this MCMC step by reformulating both Gibbs updates as Gaussian denoising problems and implementing them through ODE diffusion. The prior step reuses a pretrained denoiser, while the likelihood denoiser exploits known likelihood structure through a lightweight deep-unfolded network. Experiments on nonlinear phase retrieval demonstrate the effectiveness of the proposed method as an alternative to MCMC-based split Gibbs at lower likelihood-update cost.