A number of methods have been proposed for causal effect estimation, yet few have demonstrated efficacy in handling data with complex structures, such as images. To fill this gap, we propose Causal Multi-task Deep Ensemble (CMDE), a novel framework that learns both shared and group-specific information from the study population. We provide proofs demonstrating equivalency of CDME to a multi-task Gaussian process (GP) with a coregionalization kernel a priori. Compared to multi-task GP, CMDE efficiently handles high-dimensional and multi-modal covariates and provides pointwise uncertainty estimates of causal effects. We evaluate our method across various types of datasets and tasks and find that CMDE outperforms state-of-the-art methods on a majority of these tasks.

Diffusion models have emerged as one of the most promising frameworks for deep generative modeling. In this work, we explore the potential of non-uniform diffusion models. We show that non-uniform diffusion leads to multi-scale diffusion models which have similar structure to this of multi-scale normalizing flows. We experimentally find that in the same or less training time, the multi-scale diffusion model achieves better FID score than the standard uniform diffusion model. More importantly, it generates samples $4.4$ times faster in $128\times 128$ resolution. The speed-up is expected to be higher in higher resolutions where more scales are used. Moreover, we show that non-uniform diffusion leads to a novel estimator for the conditional score function which achieves on par performance with the state-of-the-art conditional denoising estimator. Our theoretical and experimental findings are accompanied by an open source library MSDiff which can facilitate further research of non-uniform diffusion models.

Score-based diffusion models have emerged as one of the most promising frameworks for deep generative modelling. In this work we conduct a systematic comparison and theoretical analysis of different approaches to learning conditional probability distributions with score-based diffusion models. In particular, we prove results which provide a theoretical justification for one of the most successful estimators of the conditional score. Moreover, we introduce a multi-speed diffusion framework, which leads to a new estimator for the conditional score, performing on par with previous state-of-the-art approaches. Our theoretical and experimental findings are accompanied by an open source library MSDiff which allows for application and further research of multi-speed diffusion models.