Diffusion Models as Cartoonists! The Curious Case of High Density Regions

We investigate what kind of images lie in the high-density regions of diffusion models. We introduce a theoretical mode-tracking process capable of pinpointing the exact mode of the denoising distribution, and we propose a practical high-probability sampler that consistently generates images of higher likelihood than usual samplers. Our empirical findings reveal the existence of significantly higher likelihood samples that typical samplers do not produce, often manifesting as cartoon-like drawings or blurry images depending on the noise level. Curiously, these patterns emerge in datasets devoid of such examples. We also present a novel approach to track sample likelihoods in diffusion SDEs, which remarkably incurs no additional computational cost.

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.

What Ails Generative Structure-based Drug Design: Too Little or Too Much Expressivity?

Several generative models with elaborate training and sampling procedures have been proposed recently to accelerate structure-based drug design (SBDD); however, perplexingly, their empirical performance turns out to be suboptimal. We seek to better understand this phenomenon from both theoretical and empirical perspectives. Since most of these models apply graph neural networks (GNNs), one may suspect that they inherit the representational limitations of GNNs. We analyze this aspect, establishing the first such results for protein-ligand complexes. A plausible counterview may attribute the underperformance of these models to their excessive parameterizations, inducing expressivity at the expense of generalization. We also investigate this possibility with a simple metric-aware approach that learns an economical surrogate for affinity to infer an unlabelled molecular graph and optimizes for labels conditioned on this graph and molecular properties. The resulting model achieves state-of-the-art results using 100x fewer trainable parameters and affords up to 1000x speedup. Collectively, our findings underscore the need to reassess and redirect the existing paradigm and efforts for SBDD.

Improving robustness to corruptions with multiplicative weight perturbations

Deep neural networks (DNNs) excel on clean images but struggle with corrupted ones. Incorporating specific corruptions into the data augmentation pipeline can improve robustness to those corruptions but may harm performance on clean images and other types of distortion. In this paper, we introduce an alternative approach that improves the robustness of DNNs to a wide range of corruptions without compromising accuracy on clean images. We first demonstrate that input perturbations can be mimicked by multiplicative perturbations in the weight space. Leveraging this, we propose Data Augmentation via Multiplicative Perturbation (DAMP), a training method that optimizes DNNs under random multiplicative weight perturbations. We also examine the recently proposed Adaptive Sharpness-Aware Minimization (ASAM) and show that it optimizes DNNs under adversarial multiplicative weight perturbations. Experiments on image classification datasets (CIFAR-10/100, TinyImageNet and ImageNet) and neural network architectures (ResNet50, ViT-S/16) show that DAMP enhances model generalization performance in the presence of corruptions across different settings. Notably, DAMP is able to train a ViT-S/16 on ImageNet from scratch, reaching the top-1 error of 23.7% which is comparable to ResNet50 without extensive data augmentations.

Robust Classification by Coupling Data Mollification with Label Smoothing

Introducing training-time augmentations is a key technique to enhance generalization and prepare deep neural networks against test-time corruptions. Inspired by the success of generative diffusion models, we propose a novel approach coupling data augmentation, in the form of image noising and blurring, with label smoothing to align predicted label confidences with image degradation. The method is simple to implement, introduces negligible overheads, and can be combined with existing augmentations. We demonstrate improved robustness and uncertainty quantification on the corrupted image benchmarks of the CIFAR and TinyImageNet datasets.

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.

ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs

Climate and weather prediction traditionally relies on complex numerical simulations of atmospheric physics. Deep learning approaches, such as transformers, have recently challenged the simulation paradigm with complex network forecasts. However, they often act as data-driven black-box models that neglect the underlying physics and lack uncertainty quantification. We address these limitations with ClimODE, a spatiotemporal continuous-time process that implements a key principle of advection from statistical mechanics, namely, weather changes due to a spatial movement of quantities over time. ClimODE models precise weather evolution with value-conserving dynamics, learning global weather transport as a neural flow, which also enables estimating the uncertainty in predictions. Our approach outperforms existing data-driven methods in global and regional forecasting with an order of magnitude smaller parameterization, establishing a new state of the art.

Field-based Molecule Generation

This work introduces FMG, a field-based model for drug-like molecule generation. We show how the flexibility of this method provides crucial advantages over the prevalent, point-cloud based methods, and achieves competitive molecular stability generation. We tackle optical isomerism (enantiomers), a previously omitted molecular property that is crucial for drug safety and effectiveness, and thus account for all molecular geometry aspects. We demonstrate how previous methods are invariant to a group of transformations that includes enantiomer pairs, leading them invariant to the molecular R and S configurations, while our field-based generative model captures this property.

Understanding deep neural networks through the lens of their non-linearity

The remarkable success of deep neural networks (DNN) is often attributed to their high expressive power and their ability to approximate functions of arbitrary complexity. Indeed, DNNs are highly non-linear models, and activation functions introduced into them are largely responsible for this. While many works studied the expressive power of DNNs through the lens of their approximation capabilities, quantifying the non-linearity of DNNs or of individual activation functions remains an open problem. In this paper, we propose the first theoretically sound solution to track non-linearity propagation in deep neural networks with a specific focus on computer vision applications. Our proposed affinity score allows us to gain insights into the inner workings of a wide range of different architectures and learning paradigms. We provide extensive experimental results that highlight the practical utility of the proposed affinity score and its potential for long-reaching applications.