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.

Disentangled representation learning (DRL) aims to identify and decompose underlying factors behind observations, thus facilitating data perception and generation.

However, existing models are generally modality-dependent, requiring custom architectures and objectives to process different classes of signals.

Deep neural networks have been used widely to learn the latent structure of datasets, across modalities such as images, shapes, and audio signals. However, existing models are generally modality-dependent, requiring custom architectures and objectives to process different classes of signals. We leverage neural fields to capture the underlying structure in image, shape, audio and cross-modal audiovisual domains in a modality-independent manner. We cast our task as one of learning a manifold, where we aim to infer a low-dimensional, locally linear subspace in which our data resides. By enforcing coverage of the manifold, local linearity, and local isometry, our model -- dubbed GEM -- learns to capture the underlying structure of datasets across modalities. We can then travel along linear regions of our manifold to obtain perceptually consistent interpolations between samples, and can further use GEM to recover points on our manifold and glean not only diverse completions of input images, but cross-modal hallucinations of audio or image signals. Finally, we show that by walking across the underlying manifold of GEM, we may generate new samples in our signal domains.

As machine learning becomes increasingly central to molecular design, it is vital to ensure the reliability of learnable protein-ligand scoring functions on novel protein targets. While many scoring functions perform well on standard benchmarks, their ability to generalize beyond training data remains a significant challenge. In this work, we evaluate the generalization capability of state-of-the-art scoring functions on dataset splits that simulate evaluation on targets with a limited number of known structures and experimental affinity measurements. Our analysis reveals that the commonly used benchmarks do not reflect the true challenge of generalizing to novel targets. We also investigate whether large-scale self-supervised pretraining can bridge this generalization gap and we provide preliminary evidence of its potential. Furthermore, we probe the efficacy of simple methods that leverage limited test-target data to improve scoring function performance. Our findings underscore the need for more rigorous evaluation protocols and offer practical guidance for designing scoring functions with predictive power extending to novel protein targets.