Conditional generation sometimes relies on structural knowledge that is not fully represented in the training data. This thesis studies two ways such knowledge can enter a generative model: as an inference-time rule for constructing an unseen target distribution and as a training-time inductive bias.

The first project studies inference-time composition of learned diffusion scores. Under independent causal mechanisms, a compound intervention can be identified at the clean-data level as a geometric composition of single-intervention distributions. However, this identification result does not imply that the same score composition is exact at intermediate diffusion times. We distinguish approximation error, caused by the noncommutativity of noising and composition, from estimation error in the learned source scores. In the controlled analytical and empirical settings studied here, estimation error can dominate when the composed target lies in low-density regions of the source distributions. In these settings, Feynman–Kac Correctors may reduce sampling approximation error while worsening final sample quality by more faithfully following an inaccurate learned composition.

The second project considers multimodal vessel trajectory prediction under a domain-informed directional prior: environmental context influences vessel dynamics over the forecasting horizon, whereas vessel motion does not meaningfully determine the surrounding mesoscale environment. The main contribution is the Conditional Informer, which encodes this asymmetry through directional cross-attention while preserving vessel state as the primary prediction stream. We use standard modality masking during training to evaluate the same architecture under different patterns of auxiliary-input availability. In the dataset and deployment conditions considered, the results suggest that the architectural prior provides a useful organization of contextual information, while exposure to missing-modality cases is still needed for robust fallback when auxiliary inputs are absent.

Together, the two projects examine distinct ways of incorporating structural knowledge into conditional generation: through inference-time composition in diffusion models and through architectural design in multimodal trajectory forecasting.

49 pages

Thesis Committee:
Pradeep Ravikumar (Chair)
Bryan Wilder

Jignesh Patel, Interim Head, Computer Science Department
Martial Hebert, Dean, School of Computer Science

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