To achieve the highest perceptual quality, state-of-the-art diffusion models are optimized with objectives that typically look very different from the maximum likelihood and the Evidence Lower Bound (ELBO) objectives. In this work, we reveal that diffusion model objectives are actually closely related to the ELBO.Specifically, we show that all commonly used diffusion model objectives equate to a weighted integral of ELBOs over different noise levels, where the weighting depends on the specific objective used. Under the condition of monotonic weighting, the connection is even closer: the diffusion objective then equals the ELBO, combined with simple data augmentation, namely Gaussian noise perturbation. We show that this condition holds for a number of state-of-the-art diffusion models. In experiments, we explore new monotonic weightings and demonstrate their effectiveness, achieving state-of-the-art FID scores on the high-resolution ImageNet benchmark.

Diffusion models have achieved remarkable success in generating high-resolution, realistic images across diverse natural distributions. However, their performance heavily relies on high-quality training data, making it challenging to learn meaningful distributions from corrupted samples. This limitation restricts their applicability in scientific domains where clean data is scarce or costly to obtain. In this work, we introduce denoising score distillation (DSD), a surprisingly effective and novel approach for training high-quality generative models from low-quality data. DSD first pretrains a diffusion model exclusively on noisy, corrupted samples and then distills it into a one-step generator capable of producing refined, clean outputs. While score distillation is traditionally viewed as a method to accelerate diffusion models, we show that it can also significantly enhance sample quality, particularly when starting from a degraded teacher model. Across varying noise levels and datasets, DSD consistently improves generative performance--we summarize our empirical evidence in Figure 1. Furthermore, we provide theoretical insights showing that, in a linear model setting, DSD identifies the eigenspace of the clean data distribution's covariance matrix, implicitly regularizing the generator. This perspective reframes score distillation as not only a tool for efficiency but also a mechanism for improving generative models, particularly in low-quality data settings.

To achieve the highest perceptual quality, state-of-the-art diffusion models are optimized with objectives that typically look very different from the maximum likelihood and the Evidence Lower Bound (ELBO) objectives. In this work, we reveal that diffusion model objectives are actually closely related to the ELBO.Specifically, we show that all commonly used diffusion model objectives equate to a weighted integral of ELBOs over different noise levels, where the weighting depends on the specific objective used. Under the condition of monotonic weighting, the connection is even closer: the diffusion objective then equals the ELBO, combined with simple data augmentation, namely Gaussian noise perturbation. We show that this condition holds for a number of state-of-the-art diffusion models. In experiments, we explore new monotonic weightings and demonstrate their effectiveness, achieving state-of-the-art FID scores on the high-resolution ImageNet benchmark.

In this paper, we explore a new generative approach for learning visual representations. Our method, DARL, employs a decoder-only Transformer to predict image patches autoregressively. We find that training with Mean Squared Error (MSE) alone leads to strong representations. To enhance the image generation ability, we replace the MSE loss with the diffusion objective by using a denoising patch decoder. We show that the learned representation can be improved by using tailored noise schedules and longer training in larger models. Notably, the optimal schedule differs significantly from the typical ones used in standard image diffusion models. Overall, despite its simple architecture, DARL delivers performance remarkably close to state-of-the-art masked prediction models under the fine-tuning protocol. This marks an important step towards a unified model capable of both visual perception and generation, effectively combining the strengths of autoregressive and denoising diffusion models.

Despite the growing popularity of diffusion models, gaining a deep understanding of the model class remains somewhat elusive for the uninitiated in non-equilibrium statistical physics. With that in mind, we present what we believe is a more straightforward introduction to diffusion models using directed graphical modelling and variational Bayesian principles, which imposes relatively fewer prerequisites on the average reader. Our exposition constitutes a comprehensive technical review spanning from foundational concepts like deep latent variable models to recent advances in continuous-time diffusion-based modelling, highlighting theoretical connections between model classes along the way. We provide additional mathematical insights that were omitted in the seminal works whenever possible to aid in understanding, while avoiding the introduction of new notation. We envision this article serving as a useful educational supplement for both researchers and practitioners in the area, and we welcome feedback and contributions from the community at https://github.com/biomedia-mira/demystifying-diffusion.

Detecting misleading patterns in automated diagnostic assistance systems, such as those powered by Artificial Intelligence, is critical to ensuring their reliability, particularly in healthcare. Current techniques for evaluating deep learning models cannot visualize confounding factors at a diagnostic level. Here, we propose a self-conditioned diffusion model termed DiffChest and train it on a dataset of 515,704 chest radiographs from 194,956 patients from multiple healthcare centers in the United States and Europe. DiffChest explains classifications on a patient-specific level and visualizes the confounding factors that may mislead the model. We found high inter-reader agreement when evaluating DiffChest's capability to identify treatment-related confounders, with Fleiss' Kappa values of 0.8 or higher across most imaging findings. Confounders were accurately captured with 11.1% to 100% prevalence rates. Furthermore, our pretraining process optimized the model to capture the most relevant information from the input radiographs. DiffChest achieved excellent diagnostic accuracy when diagnosing 11 chest conditions, such as pleural effusion and cardiac insufficiency, and at least sufficient diagnostic accuracy for the remaining conditions. Our findings highlight the potential of pretraining based on diffusion models in medical image classification, specifically in providing insights into confounding factors and model robustness.