Lea Bogensperger

Lea Bogensperger, Dominik Narnhofer, Filip Ilic et al.

Medical image segmentation is a crucial task that relies on the ability to accurately identify and isolate regions of interest in medical images. Thereby, generative approaches allow to capture the statistical properties of segmentation masks that are dependent on the respective structures. In this work we propose a conditional score-based generative modeling framework to represent the signed distance function (SDF) leading to an implicit distribution of segmentation masks. The advantage of leveraging the SDF is a more natural distortion when compared to that of binary masks. By learning the score function of the conditional distribution of SDFs we can accurately sample from the distribution of segmentation masks, allowing for the evaluation of statistical quantities. Thus, this probabilistic representation allows for the generation of uncertainty maps represented by the variance, which can aid in further analysis and enhance the predictive robustness. We qualitatively and quantitatively illustrate competitive performance of the proposed method on a public nuclei and gland segmentation data set, highlighting its potential utility in medical image segmentation applications.

Christoph Griesbacher, Lea Bogensperger, Andreas Habring et al.

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.

Amaru Caceres Arroyo, Lea Bogensperger, Ahmed Allam et al.

Protein fitness optimization is challenged by a vast combinatorial landscape where high-fitness variants are extremely sparse. Many current methods either underperform or require computationally expensive gradient-based sampling. We present CHASE, a framework that repurposes the evolutionary knowledge of pretrained protein language models by compressing their embeddings into a compact latent space. By training a conditional flow-matching model with classifier-free guidance, we enable the direct generation of high-fitness variants without predictor-based guidance during the ODE sampling steps. CHASE achieves state-of-the-art performance on AAV and GFP protein design benchmarks. Finally, we show that bootstrapping with synthetic data can further enhance performance in data-constrained settings.

Michal Balcerak, Tamaz Amiranashvili, Antonio Terpin et al.

Current state-of-the-art generative models map noise to data distributions by matching flows or scores. A key limitation of these models is their inability to readily integrate available partial observations and additional priors. In contrast, energy-based models (EBMs) address this by incorporating corresponding scalar energy terms. Here, we propose Energy Matching, a framework that endows flow-based approaches with the flexibility of EBMs. Far from the data manifold, samples move from noise to data along irrotational, optimal transport paths. As they approach the data manifold, an entropic energy term guides the system into a Boltzmann equilibrium distribution, explicitly capturing the underlying likelihood structure of the data. We parameterize these dynamics with a single time-independent scalar field, which serves as both a powerful generator and a flexible prior for effective regularization of inverse problems. The present method substantially outperforms existing EBMs on CIFAR-10 and ImageNet generation in terms of fidelity, while retaining simulation-free training of transport-based approaches away from the data manifold. Furthermore, we leverage the flexibility of the method to introduce an interaction energy that supports the exploration of diverse modes, which we demonstrate in a controlled protein generation setting. This approach learns a scalar potential energy, without time conditioning, auxiliary generators, or additional networks, marking a significant departure from recent EBM methods. We believe this simplified yet rigorous formulation significantly advances EBMs capabilities and paves the way for their wider adoption in generative modeling in diverse domains.

Arnela Hadzic, Lea Bogensperger, Simon Johannes Joham et al.

Deep learning techniques for anatomical landmark localization (ALL) have shown great success, but their reliance on large annotated datasets remains a problem due to the tedious and costly nature of medical data acquisition and annotation. While traditional data augmentation, variational autoencoders (VAEs), and generative adversarial networks (GANs) have already been used to synthetically expand medical datasets, diffusion-based generative models have recently started to gain attention for their ability to generate high-quality synthetic images. In this study, we explore the use of denoising diffusion probabilistic models (DDPMs) for generating medical images and their corresponding heatmaps of landmarks to enhance the training of a supervised deep learning model for ALL. Our novel approach involves a DDPM with a 2-channel input, incorporating both the original medical image and its heatmap of annotated landmarks. We also propose a novel way to assess the quality of the generated images using a Markov Random Field (MRF) model for landmark matching and a Statistical Shape Model (SSM) to check landmark plausibility, before we evaluate the DDPM-augmented dataset in the context of an ALL task involving hand X-Rays.

Lea Bogensperger, Dominik Narnhofer, Ahmed Allam et al.

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.

Lea Bogensperger, Matthias J. Ehrhardt, Thomas Pock et al.

We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level problem). We utilize an iterative algorithm called `piggyback' to compute the gradient of the loss and minimizer of the lower-level problem. Given that the lower-level problem is solved numerically, the loss function and thus its gradient can only be computed inexactly. To estimate the accuracy of the computed hypergradient, we derive an a-posteriori error bound, which provides guides for setting the tolerance for the lower-level problem, as well as the piggyback algorithm. To efficiently solve the upper-level optimization, we also propose an adaptive method for choosing a suitable step-size. To illustrate the proposed method, we consider a few learned regularizer problems, such as training an input-convex neural network.

Arnela Hadzic, Franz Thaler, Lea Bogensperger et al.

Flow matching has emerged as a promising generative approach that addresses the lengthy sampling times associated with state-of-the-art diffusion models and enables a more flexible trajectory design, while maintaining high-quality image generation. This capability makes it suitable as a generative prior for image restoration tasks. Although current methods leveraging flow models have shown promising results in restoration, some still suffer from long processing times or produce over-smoothed results. To address these challenges, we introduce Restora-Flow, a training-free method that guides flow matching sampling by a degradation mask and incorporates a trajectory correction mechanism to enforce consistency with degraded inputs. We evaluate our approach on both natural and medical datasets across several image restoration tasks involving a mask-based degradation, i.e., inpainting, super-resolution and denoising. We show superior perceptual quality and processing time compared to diffusion and flow matching-based reference methods.

Jin-Young Kim, Hyojun Go, Lea Bogensperger et al.

MeanFlow promises high-quality generative modeling in few steps, by jointly learning instantaneous and average velocity fields. Yet, the underlying training dynamics remain unclear. We analyze the interaction between the two velocities and find: (i) well-established instantaneous velocity is a prerequisite for learning average velocity; (ii) learning of instantaneous velocity benefits from average velocity when the temporal gap is small, but degrades as the gap increases; and (iii) task-affinity analysis indicates that smooth learning of large-gap average velocities, essential for one-step generation, depends on the prior formation of accurate instantaneous and small-gap average velocities. Guided by these observations, we design an effective training scheme that accelerates the formation of instantaneous velocity, then shifts emphasis from short- to long-interval average velocity. Our enhanced MeanFlow training yields faster convergence and significantly better few-step generation: With the same DiT-XL backbone, our method reaches an impressive FID of 2.87 on 1-NFE ImageNet 256x256, compared to 3.43 for the conventional MeanFlow baseline. Alternatively, our method matches the performance of the MeanFlow baseline with 2.5x shorter training time, or with a smaller DiT-L backbone.