Related papers: Implicit Regularisation in Diffusion Models: An Al…
We theoretically investigate the phenomena of generalization and memorization in diffusion models. Empirical studies suggest that these phenomena are influenced by model complexity and the size of the training dataset. In our experiments,…
Diffusion models have become a leading paradigm in generative AI, with score estimation via denoising score matching as a central component. While recent theory provides strong statistical guarantees, it typically relies on…
How diffusion models generalize beyond their training set is not known, and is somewhat mysterious given two facts: the optimum of the denoising score matching (DSM) objective usually used to train diffusion models is the score function of…
Diffusion models generalize well in practice. However, an optimal diffusion model fully memorizes the training data and therefore fails to generalize, raising the question of what induces generalization in a real diffusion model. We show…
In this work, we study the generalizability of diffusion models by looking into the hidden properties of the learned score functions, which are essentially a series of deep denoisers trained on various noise levels. We observe that as…
We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…
In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often…
Score-based generative models (SGMs) have emerged as one of the most popular classes of generative models. A substantial body of work now exists on the analysis of SGMs, focusing either on discretization aspects or on their statistical…
We propose a simple, training-free mechanism which explains the generalization behaviour of diffusion models. By comparing pre-trained diffusion models to their theoretically optimal empirical counterparts, we identify a shared local…
Diffusion models have emerged as a powerful framework for generative modeling. At the heart of the methodology is score matching: learning gradients of families of log-densities for noisy versions of the data distribution at different…
Deep neural networks (DNNs) trained for image denoising are able to generate high-quality samples with score-based reverse diffusion algorithms. These impressive capabilities seem to imply an escape from the curse of dimensionality, but…
Diffusion models achieve remarkable generation quality, yet face a fundamental challenge known as memorization, where generated samples can replicate training samples exactly. We develop a theoretical framework to explain this phenomenon by…
Many recent works utilize denoising score matching to optimize the conditional input of diffusion models. In this workshop paper, we demonstrate that such optimization breaks the equivalence between denoising score matching and exact score…
Algorithmic stability is an established tool for analyzing generalization. While adversarial training enhances model robustness, it often suffers from robust overfitting and an enlarged generalization gap. Although recent work has…
A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…
Diffusion models are gaining widespread use in cutting-edge image, video, and audio generation. Score-based diffusion models stand out among these methods, necessitating the estimation of score function of the input data distribution. In…
We study the inductive biases of diffusion models with a conditioning-variable, which have seen widespread application as both text-conditioned generative image models and observation-conditioned continuous control policies. We observe that…
Denoising score matching plays a pivotal role in the performance of diffusion-based generative models. However, the empirical optimal score--the exact solution to the denoising score matching--leads to memorization, where generated samples…
We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals --…
Despite their success in image generation, diffusion models can memorize training data, raising serious privacy and copyright concerns. Although prior work has sought to characterize, detect, and mitigate memorization, the fundamental…