Free Hunch: Denoiser Covariance Estimation for Diffusion Models Without Extra Costs

The covariance for clean data given a noisy observation is an important quantity in many conditional generation methods for diffusion models. Current methods require heavy test-time computation, altering the standard diffusion training process or denoiser architecture, or making heavy approximations. We propose a new framework that sidesteps these issues by using covariance information that is available for free from training data and the curvature of the generative trajectory, which is linked to the covariance through the second-order Tweedie's formula. We integrate these sources of information using {\em (i)} a novel method to transfer covariance estimates across noise levels and (ii) low-rank updates in a given noise level. We validate the method on linear inverse problems, where it outperforms recent baselines, especially with fewer diffusion steps.

Improving Discrete Diffusion Models via Structured Preferential Generation

In the domains of image and audio, diffusion models have shown impressive performance. However, their application to discrete data types, such as language, has often been suboptimal compared to autoregressive generative models. This paper tackles the challenge of improving discrete diffusion models by introducing a structured forward process that leverages the inherent information hierarchy in discrete categories, such as words in text. Our approach biases the generative process to produce certain categories before others, resulting in a notable improvement in log-likelihood scores on the text8 dataset. This work paves the way for more advances in discrete diffusion models with potentially significant enhancements in performance.

Alignment is Key for Applying Diffusion Models to Retrosynthesis

Retrosynthesis, the task of identifying precursors for a given molecule, can be naturally framed as a conditional graph generation task. Diffusion models are a particularly promising modelling approach, enabling post-hoc conditioning and trading off quality for speed during generation. We show mathematically that permutation equivariant denoisers severely limit the expressiveness of graph diffusion models and thus their adaptation to retrosynthesis. To address this limitation, we relax the equivariance requirement such that it only applies to aligned permutations of the conditioning and the generated graphs obtained through atom mapping. Our new denoiser achieves the highest top-$1$ accuracy ($54.7$\%) across template-free and template-based methods on USPTO-50k. We also demonstrate the ability for flexible post-training conditioning and good sample quality with small diffusion step counts, highlighting the potential for interactive applications and additional controls for multi-step planning.

Generative Modelling With Inverse Heat Dissipation

While diffusion models have shown great success in image generation, their noise-inverting generative process does not explicitly consider the structure of images, such as their inherent multi-scale nature. Inspired by diffusion models and the desirability of coarse-to-fine modelling, we propose a new model that generates images through iteratively inverting the heat equation, a PDE that locally erases fine-scale information when run over the 2D plane of the image. In our novel methodology, the solution of the forward heat equation is interpreted as a variational approximation in a directed graphical model. We demonstrate promising image quality and point out emergent qualitative properties not seen in diffusion models, such as disentanglement of overall colour and shape in images and aspects of neural network interpretability. Spectral analysis on natural images positions our model as a type of dual to diffusion models and reveals implicit inductive biases in them.

A Critical Look At The Identifiability of Causal Effects with Deep Latent Variable Models

Using deep latent variable models in causal inference has attracted considerable interest recently, but an essential open question is their identifiability. While they have yielded promising results and theory exists on the identifiability of some simple model formulations, we also know that causal effects cannot be identified in general with latent variables. We investigate this gap between theory and empirical results with theoretical considerations and extensive experiments under multiple synthetic and real-world data sets, using the causal effect variational autoencoder (CEVAE) as a case study. While CEVAE seems to work reliably under some simple scenarios, it does not identify the correct causal effect with a misspecified latent variable or a complex data distribution, as opposed to the original goals of the model. Our results show that the question of identifiability cannot be disregarded, and we argue that more attention should be paid to it in future work.