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Thomas Pock

Thomas Pock contributes to research discovery and scholarly infrastructure.

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Computer Vision Machine Learning math.OC math.NA Numerical Analysis Computation eess.IV math.PR math.ST

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preprint2026arXiv

Generating Physically Consistent Molecules with Energy-Based Models

Molecules in equilibrium follow a Boltzmann distribution, making the underlying energy landscape a physically grounded modeling objective. However, such landscapes are difficult to learn from data and, once learned, hard to sample from. Diffusion and flow-matching models sidestep these difficulties by learning a time-conditional score or transport field between noise and data, losing the energy inductive bias in exchange for a more tractable training objective. We introduce EBMol, an energy-based model (EBM) that restores this inductive bias by learning an atom-additive scalar potential without explicit simulation during training. Our method employs a flow-inspired Restoring Field Matching objective to approximate the energy landscape. We adopt the Mirror-Langevin algorithm for sampling, enabling unified updates of atomic positions and types, and incorporate parallel tempering for inference-time compute scaling. EBMol is the first EBM for 3D molecular generation to achieve state-of-the-art performance on QM9 and GEOM-Drugs. Moreover, we show that the learned energy landscape serves as a principled quality metric for ranking and filtering configurations, and demonstrate controllable generation without retraining through shape-steered sampling via potential composition and zero-shot linker design.

preprint2026arXiv

Product-of-Gaussian-Mixture Diffusion Models for Joint Nonlinear MRI Reconstruction

Recently, diffusion models have attracted considerable attention for magnetic resonance image reconstruction due to their high sample quality. However, most existing methods rely on large networks with opaque time-conditioning mechanisms, and require offline coil sensitivity estimation. This results in limited interpretability of the reconstruction process and reduced flexibility in the acquisition setup. To address these limitations, we jointly reconstruct the image and the coil sensitivities by combining the parameter-efficient product-of-Gaussian-mixture diffusion model as an image prior with a classical smoothness prior on the coil sensitivities. The proposed method is fast and robust to both contrast and anatomical distribution shifts as well as changing k-space trajectories. Finally, we propose a more expressive parameterization of the image prior which improves results in denoising and magnetic resonance image reconstruction.

preprint2026arXiv

Time-Inhomogeneous Preconditioned Langevin Dynamics

Langevin sampling from distributions of the form $p(x) \propto \exp(-Ψ(x))$ faces two major challenges: (global) mode coverage and (local) mode exploration. The first challenge is particularly relevant for multi-modal distributions with disjoint modes, whereas the second arises when the potential $Ψ$ exhibits diverse and ill-conditioned local mode geometry. To address these challenges, a common approach is to precondition Langevin dynamics with problem-specific information, such as the sample covariance or the local curvature of $Ψ$. However, existing preconditioner choices inherently involve a trade-off between global mode coverage and local mode exploration, and no prior method resolves both simultaneously. To overcome this limitation, we propose the TIPreL, which introduces a time- and position-dependent preconditioner. This design effectively addresses both challenges mentioned above within a single framework. We establish convergence of the resulting dynamics in the Wasserstein-2 distance both in continuous time and for a tamed Euler discretization. In particular, our analysis extends the existing state of the art by proving convergence under time- and space-dependent diffusion coefficients, and only locally Lipschitz drifts, which has not been covered by prior work. Finally, we experimentally compare TIPreL with competing preconditioning schemes on a two-dimensional, severely ill-posed example and on a Bayesian logistic regression task in higher dimensions, confirming the efficiency of the proposed method.

preprint2022arXiv

Computed Tomography Reconstruction using Generative Energy-Based Priors

In the past decades, Computed Tomography (CT) has established itself as one of the most important imaging techniques in medicine. Today, the applicability of CT is only limited by the deposited radiation dose, reduction of which manifests in noisy or incomplete measurements. Thus, the need for robust reconstruction algorithms arises. In this work, we learn a parametric regularizer with a global receptive field by maximizing it's likelihood on reference CT data. Due to this unsupervised learning strategy, our trained regularizer truly represents higher-level domain statistics, which we empirically demonstrate by synthesizing CT images. Moreover, this regularizer can easily be applied to different CT reconstruction problems by embedding it in a variational framework, which increases flexibility and interpretability compared to feed-forward learning-based approaches. In addition, the accompanying probabilistic perspective enables experts to explore the full posterior distribution and may quantify uncertainty of the reconstruction approach. We apply the regularizer to limited-angle and few-view CT reconstruction problems, where it outperforms traditional reconstruction algorithms by a large margin.

preprint2022arXiv

Is Appearance Free Action Recognition Possible?

Intuition might suggest that motion and dynamic information are key to video-based action recognition. In contrast, there is evidence that state-of-the-art deep-learning video understanding architectures are biased toward static information available in single frames. Presently, a methodology and corresponding dataset to isolate the effects of dynamic information in video are missing. Their absence makes it difficult to understand how well contemporary architectures capitalize on dynamic vs. static information. We respond with a novel Appearance Free Dataset (AFD) for action recognition. AFD is devoid of static information relevant to action recognition in a single frame. Modeling of the dynamics is necessary for solving the task, as the action is only apparent through consideration of the temporal dimension. We evaluated 11 contemporary action recognition architectures on AFD as well as its related RGB video. Our results show a notable decrease in performance for all architectures on AFD compared to RGB. We also conducted a complimentary study with humans that shows their recognition accuracy on AFD and RGB is very similar and much better than the evaluated architectures on AFD. Our results motivate a novel architecture that revives explicit recovery of optical flow, within a contemporary design for best performance on AFD and RGB.

preprint2020arXiv

Belief Propagation Reloaded: Learning BP-Layers for Labeling Problems

It has been proposed by many researchers that combining deep neural networks with graphical models can create more efficient and better regularized composite models. The main difficulties in implementing this in practice are associated with a discrepancy in suitable learning objectives as well as with the necessity of approximations for the inference. In this work we take one of the simplest inference methods, a truncated max-product Belief Propagation, and add what is necessary to make it a proper component of a deep learning model: We connect it to learning formulations with losses on marginals and compute the backprop operation. This BP-Layer can be used as the final or an intermediate block in convolutional neural networks (CNNs), allowing us to design a hierarchical model composing BP inference and CNNs at different scale levels. The model is applicable to a range of dense prediction problems, is well-trainable and provides parameter-efficient and robust solutions in stereo, optical flow and semantic segmentation.

preprint2020arXiv

Image Morphing in Deep Feature Spaces: Theory and Applications

This paper combines image metamorphosis with deep features. To this end, images are considered as maps into a high-dimensional feature space and a structure-sensitive, anisotropic flow regularization is incorporated in the metamorphosis model proposed by Miller, Trouvé, Younes and coworkers. For this model a variational time discretization of the Riemannian path energy is presented and the existence of discrete geodesic paths minimizing this energy is demonstrated. Furthermore, convergence of discrete geodesic paths to geodesic paths in the time continuous model is investigated. The spatial discretization is based on a finite difference approximation in image space and a stable spline approximation in deformation space, the fully discrete model is optimized using the iPALM algorithm. Numerical experiments indicate that the incorporation of semantic deep features is superior to intensity-based approaches.

preprint2020arXiv

Improving Optical Flow on a Pyramid Level

In this work we review the coarse-to-fine spatial feature pyramid concept, which is used in state-of-the-art optical flow estimation networks to make exploration of the pixel flow search space computationally tractable and efficient. Within an individual pyramid level, we improve the cost volume construction process by departing from a warping- to a sampling-based strategy, which avoids ghosting and hence enables us to better preserve fine flow details. We further amplify the positive effects through a level-specific, loss max-pooling strategy that adaptively shifts the focus of the learning process on under-performing predictions. Our second contribution revises the gradient flow across pyramid levels. The typical operations performed at each pyramid level can lead to noisy, or even contradicting gradients across levels. We show and discuss how properly blocking some of these gradient components leads to improved convergence and ultimately better performance. Finally, we introduce a distillation concept to counteract the issue of catastrophic forgetting and thus preserving knowledge over models sequentially trained on multiple datasets. Our findings are conceptually simple and easy to implement, yet result in compelling improvements on relevant error measures that we demonstrate via exhaustive ablations on datasets like Flying Chairs2, Flying Things, Sintel and KITTI. We establish new state-of-the-art results on the challenging Sintel and KITTI 2012 test datasets, and even show the portability of our findings to different optical flow and depth from stereo approaches.

preprint2020arXiv

PIEMAP: Personalized Inverse Eikonal Model from cardiac Electro-Anatomical Maps

Electroanatomical mapping, a keystone diagnostic tool in cardiac electrophysiology studies, can provide high-density maps of the local electric properties of the tissue. It is therefore tempting to use such data to better individualize current patient-specific models of the heart through a data assimilation procedure and to extract potentially insightful information such as conduction properties. Parameter identification for state-of-the-art cardiac models is however a challenging task. In this work, we introduce a novel inverse problem for inferring the anisotropic structure of the conductivity tensor, that is fiber orientation and conduction velocity along and across fibers, of an eikonal model for cardiac activation. The proposed method, named PIEMAP, performed robustly with synthetic data and showed promising results with clinical data. These results suggest that PIEMAP could be a useful supplement in future clinical workflows of personalized therapies.

preprint2020arXiv

Total Deep Variation for Linear Inverse Problems

Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent architectural design patterns from deep learning. We cast the learning problem as a discrete sampled optimal control problem, for which we derive the adjoint state equations and an optimality condition. By exploiting the variational structure of our approach, we perform a sensitivity analysis with respect to the learned parameters obtained from different training datasets. Moreover, we carry out a nonlinear eigenfunction analysis, which reveals interesting properties of the learned regularizer. We show state-of-the-art performance for classical image restoration and medical image reconstruction problems.

preprint2020arXiv

Total Deep Variation: A Stable Regularizer for Inverse Problems

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and a regularizer. Classically, handcrafted regularizers are used, which are commonly outperformed by state-of-the-art deep learning approaches. In this work, we combine the variational formulation of inverse problems with deep learning by introducing the data-driven general-purpose total deep variation regularizer. In its core, a convolutional neural network extracts local features on multiple scales and in successive blocks. This combination allows for a rigorous mathematical analysis including an optimal control formulation of the training problem in a mean-field setting and a stability analysis with respect to the initial values and the parameters of the regularizer. In addition, we experimentally verify the robustness against adversarial attacks and numerically derive upper bounds for the generalization error. Finally, we achieve state-of-the-art results for numerous imaging tasks.

preprint2016arXiv

Acceleration of the PDHGM on strongly convex subspaces

We propose several variants of the primal-dual method due to Chambolle and Pock. Without requiring full strong convexity of the objective functions, our methods are accelerated on subspaces with strong convexity. This yields mixed rates, $O(1/N^2)$ with respect to initialisation and $O(1/N)$ with respect to the dual sequence, and the residual part of the primal sequence. We demonstrate the efficacy of the proposed methods on image processing problems lacking strong convexity, such as total generalised variation denoising and total variation deblurring.

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