Generative modeling of topological and spatiotemporal data

Abstract

Structured data are central to modern machine learning systems, but their structure creates modeling challenges that are not present in flat vectors or single images: graphs are invariant to node ordering, visual scenes combine symbolic relations with continuous geometry, and human or driving motion evolves through interacting agents under uncertainty. This dissertation develops generative models for topological, hybrid, and spatiotemporal data by adapting how these models represent, learn, and sample structured distributions. The first part of this thesis studies topological and hybrid data. It begins with graph generation, where we bound the support of closest invariant distributions under explicit symmetry assumptions and characterize the symmetrized empirical target induced by equivariant denoising. Learning additional permuted representations can reduce performance in the studied settings. This motivates a graph diffusion model that combines flexible non-invariant denoising with permutation-invariant sampling and an efficient shifted-window graph transformer. We then extend this topological view to grounded scene graphs, where object categories, bounding boxes, and relations are generated jointly to bridge symbolic scene structure and continuous visual generation. The second part of this thesis studies motion forecasting. We formulate human trajectory prediction as conditional flow matching, enabling correlated multimodal futures to be generated together as scene-level hypotheses. We then scale this approach to autonomous-driving motion prediction by jointly producing multiple trajectories, learning confidence rankings, and improving generalization via self-conditioning. Together, these works show that generative models for structured domains become useful when structure is handled explicitly but flexibly, and identify opportunities for unified structured world models, faster samplers, and uncertainty-aware deployment.