William R. Harvey

Christian Weilbach, William Harvey, Frank Wood

We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model's performance, in terms of both training time and final accuracy. Our code can be found at https://github.com/plai-group/gsdm.

William Harvey, Saeid Naderiparizi, Vaden Masrani et al.

We present a framework for video modeling based on denoising diffusion probabilistic models that produces long-duration video completions in a variety of realistic environments. We introduce a generative model that can at test-time sample any arbitrary subset of video frames conditioned on any other subset and present an architecture adapted for this purpose. Doing so allows us to efficiently compare and optimize a variety of schedules for the order in which frames in a long video are sampled and use selective sparse and long-range conditioning on previously sampled frames. We demonstrate improved video modeling over prior work on a number of datasets and sample temporally coherent videos over 25 minutes in length. We additionally release a new video modeling dataset and semantically meaningful metrics based on videos generated in the CARLA autonomous driving simulator.

William Harvey, Frank Wood

Recent progress with conditional image diffusion models has been stunning, and this holds true whether we are speaking about models conditioned on a text description, a scene layout, or a sketch. Unconditional image diffusion models are also improving but lag behind, as do diffusion models which are conditioned on lower-dimensional features like class labels. We propose to close the gap between conditional and unconditional models using a two-stage sampling procedure. In the first stage we sample an embedding describing the semantic content of the image. In the second stage we sample the image conditioned on this embedding and then discard the embedding. Doing so lets us leverage the power of conditional diffusion models on the unconditional generation task, which we show improves FID by 25-50% compared to standard unconditional generation.

Andrew Campbell, William Harvey, Christian Weilbach et al.

We propose a new class of generative models that naturally handle data of varying dimensionality by jointly modeling the state and dimension of each datapoint. The generative process is formulated as a jump diffusion process that makes jumps between different dimensional spaces. We first define a dimension destroying forward noising process, before deriving the dimension creating time-reversed generative process along with a novel evidence lower bound training objective for learning to approximate it. Simulating our learned approximation to the time-reversed generative process then provides an effective way of sampling data of varying dimensionality by jointly generating state values and dimensions. We demonstrate our approach on molecular and video datasets of varying dimensionality, reporting better compatibility with test-time diffusion guidance imputation tasks and improved interpolation capabilities versus fixed dimensional models that generate state values and dimensions separately.

William Harvey, Saeid Naderiparizi, Frank Wood

We present a conditional variational auto-encoder (VAE) which, to avoid the substantial cost of training from scratch, uses an architecture and training objective capable of leveraging a foundation model in the form of a pretrained unconditional VAE. To train the conditional VAE, we only need to train an artifact to perform amortized inference over the unconditional VAE's latent variables given a conditioning input. We demonstrate our approach on tasks including image inpainting, for which it outperforms state-of-the-art GAN-based approaches at faithfully representing the inherent uncertainty. We conclude by describing a possible application of our inpainting model, in which it is used to perform Bayesian experimental design for the purpose of guiding a sensor.

William Harvey, Andreas Munk, Atılım Güneş Baydin et al.

We present a new approach to automatic amortized inference in universal probabilistic programs which improves performance compared to current methods. Our approach is a variation of inference compilation (IC) which leverages deep neural networks to approximate a posterior distribution over latent variables in a probabilistic program. A challenge with existing IC network architectures is that they can fail to model long-range dependencies between latent variables. To address this, we introduce an attention mechanism that attends to the most salient variables previously sampled in the execution of a probabilistic program. We demonstrate that the addition of attention allows the proposal distributions to better match the true posterior, enhancing inference about latent variables in simulators.

William Harvey, Michael Teng, Frank Wood

Hard visual attention is a promising approach to reduce the computational burden of modern computer vision methodologies. Hard attention mechanisms are typically non-differentiable. They can be trained with reinforcement learning but the high-variance training this entails hinders more widespread application. We show how hard attention for image classification can be framed as a Bayesian optimal experimental design (BOED) problem. From this perspective, the optimal locations to attend to are those which provide the greatest expected reduction in the entropy of the classification distribution. We introduce methodology from the BOED literature to approximate this optimal behaviour, and use it to generate `near-optimal' sequences of attention locations. We then show how to use such sequences to partially supervise, and therefore speed up, the training of a hard attention mechanism. Although generating these sequences is computationally expensive, they can be reused by any other networks later trained on the same task.