Video depth estimation lifts monocular video clips to 3D by inferring dense depth at every frame. Recent advances in single-image depth estimation, brought about by the rise of large foundation models and the use of synthetic training data, have fueled a renewed interest in video depth. However, naively applying a single-image depth estimator to every frame of a video disregards temporal continuity, which not only leads to flickering but may also break when camera motion causes sudden changes in depth range. An obvious and principled solution would be to build on top of video foundation models, but these come with their own limitations; including expensive training and inference, imperfect 3D consistency, and stitching routines for the fixed-length (short) outputs. We take a step back and demonstrate how to turn a single-image latent diffusion model (LDM) into a state-of-the-art video depth estimator. Our model, which we call RollingDepth, has two main ingredients: (i) a multi-frame depth estimator that is derived from a single-image LDM and maps very short video snippets (typically frame triplets) to depth snippets. (ii) a robust, optimization-based registration algorithm that optimally assembles depth snippets sampled at various different frame rates back into a consistent video. RollingDepth is able to efficiently handle long videos with hundreds of frames and delivers more accurate depth videos than both dedicated video depth estimators and high-performing single-frame models. Project page: rollingdepth.github.io.

The goal of protein fitness optimization is to discover new protein variants with enhanced fitness for a given use. The vast search space and the sparsely populated fitness landscape, along with the discrete nature of protein sequences, pose significant challenges when trying to determine the gradient towards configurations with higher fitness. We introduce *Variational Latent Generative Protein Optimization* (VLGPO), a variational perspective on fitness optimization. Our method embeds protein sequences in a continuous latent space to enable efficient sampling from the fitness distribution and combines a (learned) flow matching prior over sequence mutations with a fitness predictor to guide optimization towards sequences with high fitness. VLGPO achieves state-of-the-art results on two different protein benchmarks of varying complexity. Moreover, the variational design with explicit prior and likelihood functions offers a flexible plug-and-play framework that can be easily customized to suit various protein design tasks.

Flow-based latent generative models such as Stable Diffusion 3 are able to generate images with remarkable quality, even enabling photorealistic text-to-image generation. Their impressive performance suggests that these models should also constitute powerful priors for inverse imaging problems, but that approach has not yet led to comparable fidelity. There are several key obstacles: (i) the data likelihood term is usually intractable; (ii) learned generative models cannot be directly conditioned on the distorted observations, leading to conflicting objectives between data likelihood and prior; and (iii) the reconstructions can deviate from the observed data. We present FLAIR, a novel, training-free variational framework that leverages flow-based generative models as prior for inverse problems. To that end, we introduce a variational objective for flow matching that is agnostic to the type of degradation, and combine it with deterministic trajectory adjustments to guide the prior towards regions which are more likely under the posterior. To enforce exact consistency with the observed data, we decouple the optimization of the data fidelity and regularization terms. Moreover, we introduce a time-dependent calibration scheme in which the strength of the regularization is modulated according to off-line accuracy estimates. Results on standard imaging benchmarks demonstrate that FLAIR consistently outperforms existing diffusion- and flow-based methods in terms of reconstruction quality and sample diversity. Source code is available at https://inverseflair.github.io/.

Abstract Medical image segmentation plays an important role in accurately identifying and isolating regions of interest within medical images. Generative approaches are particularly effective in modeling the statistical properties of segmentation masks that are closely related to the respective structures. In this work we introduce FlowSDF, an image-guided conditional flow matching framework, designed to represent the signed distance function (SDF), and, in turn, to represent an implicit distribution of segmentation masks. The advantage of leveraging the SDF is a more natural distortion when compared to that of binary masks. Through the learning of a vector field associated with the probability path of conditional SDF distributions, our framework enables accurate sampling of segmentation masks and the computation of relevant statistical measures. This probabilistic approach also facilitates the generation of uncertainty maps represented by the variance, thereby supporting enhanced robustness in prediction and further analysis. We qualitatively and quantitatively illustrate competitive performance of the proposed method on a public nuclei and gland segmentation data set, highlighting its utility in medical image segmentation applications.

We propose a novel approach to video anomaly detection: we treat feature vectors extracted from videos as re-alizations of a random variable with a fixed distribution and model this distribution with a neural network. This lets us estimate the likelihood of test videos and detect video anomalies by thresholding the likelihood estimates. We train our video anomaly detector using a modification of de-noising score matching, a method that injects training data with noise to facilitate modeling its distribution. To elim-inate hyperparameter selection, we model the distribution of noisy video features across a range of noise levels and introduce a regularizer that tends to align the models for different levels of noise. At test time, we combine anomaly indications at multiple noise scales with a Gaussian mix-ture model. Running our video anomaly detector induces minimal delays as inference requires merely extracting the features and forward-propagating them through a shallow neural network and a Gaussian mixture model. Our ex-periments on five popular video anomaly detection bench-marks demonstrate state-of-the-art performance, both in the object-centric and in the frame-centric setup.

Abstract. In this work, a method for obtaining pixelwise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal prediction in order to obtain coverage guarantees for the error bounds, without making any assumption on the underlying data distribution. It is generally applicable to Bayesian regularization approaches, independent, e.g., of the concrete choice of the prior. Furthermore, the coverage guarantees can also be obtained in case only approximate sampling from the posterior is possible. With this in particular, the proposed framework is able to incorporate any learned prior in a black-box manner. Guaranteed coverage without assumptions on the underlying distributions is only achievable since the magnitude of the error bounds is, in general, unknown in advance. Nevertheless, experiments with multiple regularization approaches presented in the paper confirm that, in practice, the obtained error bounds are rather tight. For realizing the numerical experiments, a novel primal-dual Langevin algorithm for sampling from nonsmooth distributions is also introduced in this work, showing promising results in practice. While a proof of convergence for this primal-dual algorithm is still open, the theoretical guarantees of the proposed method do not require a guaranteed convergence of the sampling algorithm.

Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less frequently systematically analyzed. In this work, we introduce a Bayesian variational framework to quantify the epistemic uncertainty. To this end, we solve the linear inverse problem of undersampled MRI reconstruction in a variational setting. The associated energy functional is composed of a data fidelity term and the total deep variation (TDV) as a learned parametric regularizer. To estimate the epistemic uncertainty we draw the parameters of the TDV regularizer from a multivariate Gaussian distribution, whose mean and covariance matrix are learned in a stochastic optimal control problem. In several numerical experiments, we demonstrate that our approach yields competitive results for undersampled MRI reconstruction. Moreover, we can accurately quantify the pixelwise epistemic uncertainty, which can serve radiologists as an additional resource to visualize reconstruction reliability.