Jude Wells

Breeshey Roskams-Hieter, Jude Wells, Sara Wade

Missing data persists as a major barrier to data analysis across numerous applications. Recently, deep generative models have been used for imputation of missing data, motivated by their ability to capture highly non-linear and complex relationships in the data. In this work, we investigate the ability of deep models, namely variational autoencoders (VAEs), to account for uncertainty in missing data through multiple imputation strategies. We find that VAEs provide poor empirical coverage of missing data, with underestimation and overconfident imputations, particularly for more extreme missing data values. To overcome this, we employ $β$-VAEs, which viewed from a generalized Bayes framework, provide robustness to model misspecification. Assigning a good value of $β$ is critical for uncertainty calibration and we demonstrate how this can be achieved using cross-validation. In downstream tasks, we show how multiple imputation with $β$-VAEs can avoid false discoveries that arise as artefacts of imputation.

Umberto Borso, Davide Paglieri, Jude Wells et al.

Diffusion models have achieved state-of-the-art performance across multiple domains, with recent advancements extending their applicability to discrete data. However, aligning discrete diffusion models with task-specific preferences remains challenging, particularly in scenarios where explicit reward functions are unavailable. In this work, we introduce Discrete Diffusion DPO (D2-DPO), the first adaptation of Direct Preference Optimization (DPO) to discrete diffusion models formulated as continuous-time Markov chains. Our approach derives a novel loss function that directly fine-tunes the generative process using preference data while preserving fidelity to a reference distribution. We validate D2-DPO on a structured binary sequence generation task, demonstrating that the method effectively aligns model outputs with preferences while maintaining structural validity. Our results highlight that D2-DPO enables controlled fine-tuning without requiring explicit reward models, making it a practical alternative to reinforcement learning-based approaches. Future research will explore extending D2-DPO to more complex generative tasks, including language modeling and protein sequence generation, as well as investigating alternative noise schedules, such as uniform noising, to enhance flexibility across different applications.