Graph Energy Matching: Transport-Aligned Energy-Based Modeling for Graph Generation

Energy-based models for discrete domains, such as graphs, explicitly capture relative likelihoods, naturally enabling composable probabilistic inference tasks like conditional generation or enforcing constraints at test-time. However, discrete energy-based models typically struggle with efficient and high-quality sampling, as off-support regions often contain spurious local minima, trapping samplers and causing training instabilities. This has historically resulted in a fidelity gap relative to discrete diffusion models. We introduce Graph Energy Matching (GEM), a generative framework for graphs that closes this fidelity gap. Motivated by the transport map optimization perspective of the Jordan-Kinderlehrer-Otto (JKO) scheme, GEM learns a permutation-invariant potential energy that simultaneously provides transport-aligned guidance from noise toward data and refines samples within regions of high data likelihood. Further, we introduce a sampling protocol that leverages an energy-based switch to seamlessly bridge: (i) rapid, gradient-guided transport toward high-probability regions to (ii) a mixing regime for exploration of the learned graph distribution. On molecular graph benchmarks, GEM matches or exceeds strong discrete diffusion baselines. Beyond sample quality, explicit modeling of relative likelihood enables targeted exploration at inference time, facilitating compositional generation, property-constrained sampling, and geodesic interpolation between graphs.

ViT-AE++: Improving Vision Transformer Autoencoder for Self-supervised Medical Image Representations

Self-supervised learning has attracted increasing attention as it learns data-driven representation from data without annotations. Vision transformer-based autoencoder (ViT-AE) by He et al. (2021) is a recent self-supervised learning technique that employs a patch-masking strategy to learn a meaningful latent space. In this paper, we focus on improving ViT-AE (nicknamed ViT-AE++) for a more effective representation of both 2D and 3D medical images. We propose two new loss functions to enhance the representation during the training stage. The first loss term aims to improve self-reconstruction by considering the structured dependencies and hence indirectly improving the representation. The second loss term leverages contrastive loss to directly optimize the representation from two randomly masked views. As an independent contribution, we extended ViT-AE++ to a 3D fashion for volumetric medical images. We extensively evaluate ViT-AE++ on both natural images and medical images, demonstrating consistent improvement over vanilla ViT-AE and its superiority over other contrastive learning approaches.