Related papers: Diffusion Model for Manifold Data: Score Decomposi…
We introduce novel estimators for computing the curvature, tangent spaces, and dimension of data from manifolds, using tools from diffusion geometry. Although classical Riemannian geometry is a rich source of inspiration for geometric data…
Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
We analyze the time reversed dynamics of generative diffusion models. If the exact empirical score function is used in a regime of large dimension and exponentially large number of samples, these models are known to undergo transitions…
By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates…
The predominant success of diffusion models in generative modeling has spurred significant interest in understanding their theoretical foundations. In this work, we propose a feature learning framework aimed at analyzing and comparing the…
Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…
Score-based diffusion modeling is a generative machine learning algorithm that can be used to sample from complex distributions. They achieve this by learning a score function, i.e., the gradient of the log-probability density of the data,…
Deep Generative Models are frequently used to learn continuous representations of complex data distributions using a finite number of samples. For any generative model, including pre-trained foundation models with Diffusion or Transformer…
Diffusion models are capable of generating photo-realistic images that combine elements which likely do not appear together in the training set, demonstrating the ability to \textit{compositionally generalize}. Nonetheless, the precise…
Diffusion models have emerged as the principal paradigm for generative modeling across various domains. During training, they learn the score function, which in turn is used to generate samples at inference. They raise a basic yet unsolved…
Diffusion Models (DMs), also referred to as score-based diffusion models, utilize neural networks to specify score functions. Unlike most other probabilistic models, DMs directly model the score functions, which makes them more flexible to…
Generative models such as diffusion models have achieved remarkable success in state-of-the-art image and text tasks. Recently, score-based diffusion models have extended their success beyond image generation, showing competitive…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…
Diffusion policies have shown impressive results in robot imitation learning, even for tasks that require satisfaction of kinematic equality constraints. However, task performance alone is not a reliable indicator of the policy's ability to…
Diffusion Models are popular generative modeling methods in various vision tasks, attracting significant attention. They can be considered a unique instance of self-supervised learning methods due to their independence from label…
Understanding the structure of real data is paramount in advancing modern deep-learning methodologies. Natural data such as images are believed to be composed of features organized in a hierarchical and combinatorial manner, which neural…
This paper investigates score-based diffusion models when the underlying target distribution is concentrated on or near low-dimensional manifolds within the higher-dimensional space in which they formally reside, a common characteristic of…
Diffusion models are state-of-the-art tools for various generative tasks. Yet training these models involves estimating high-dimensional score functions, which in principle suffers from the curse of dimensionality. It is therefore important…
How do score-based generative models (SBMs) learn the data distribution supported on a low-dimensional manifold? We investigate the score model of a trained SBM through its linear approximations and subspaces spanned by local feature…