相关论文: Score Change of Variables

Diffusion models have emerged as a powerful framework in generative modeling, typically relying on optimizing neural networks to estimate the score function via forward SDE simulations. In this work, we propose an alternative method that is…

Score-based diffusion models have recently been extended to infinite-dimensional function spaces, with uses such as inverse problems arising from partial differential equations. In the Bayesian formulation of inverse problems, the aim is to…

Score-based diffusion models generate samples from a complex underlying data distribution by time-reversal of a diffusion process and represent the state-of-the-art in many generative AI applications. Here, I show how a generative diffusion…

Fourier analysis has been an instrumental tool in the development of signal processing. This leads us to wonder whether this framework could similarly benefit generative modelling. In this paper, we explore this question through the scope…

Diffusion models are widely used in applications ranging from image generation to inverse problems. However, training diffusion models typically requires clean ground-truth images, which are unavailable in many applications. We introduce…

Diffusion models are widely used as priors in imaging inverse problems. However, their performance often degrades under distribution shifts between the training and test-time images. Existing methods for identifying and quantifying…

Score-based diffusion models have emerged as one of the most promising frameworks for deep generative modelling. In this work we conduct a systematic comparison and theoretical analysis of different approaches to learning conditional…

Diffusion models have become a popular choice for representing actor policies in behavior cloning and offline reinforcement learning. This is due to their natural ability to optimize an expressive class of distributions over a continuous…

In this paper, we explore provable acceleration of diffusion models without any additional retraining. Focusing on the task of approximating a target data distribution in $\mathbb{R}^d$ to within $\varepsilon$ total-variation distance, we…

Score-based diffusion models generate new samples by learning the score function associated with a diffusion process. While the effectiveness of these models can be theoretically explained using differential equations related to the…

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…

Recently, Zhang et al. have proposed the Diffusion Exponential Integrator Sampler (DEIS) for fast generation of samples from Diffusion Models. It leverages the semi-linear nature of the probability flow ordinary differential equation (ODE)…

Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching…

Generative diffusion models synthesize new samples by reversing a diffusive process that converts a given data set to generic noise. This is accomplished by training a neural network to match the gradient of the log of the probability…

The proposed BSDE-based diffusion model represents a novel approach to diffusion modeling, which extends the application of stochastic differential equations (SDEs) in machine learning. Unlike traditional SDE-based diffusion models, our…

Many important problems in psychology and biomedical studies require testing for overdispersion, correlation and heterogeneity in mixed effects and latent variable models, and score tests are particularly useful for this purpose. But the…

This paper is a survey article of results and arguments from several of authors' papers, and it describes a new approach to global smoothing problems for dispersive and non-dispersive evolution equations based on ideas of comparison…

Near the critical point, Markov Chain Monte Carlo (MCMC) simulations of lattice quantum field theories (LQFT) become increasingly inefficient due to critical slowing down. In this work, we investigate score-based symmetry-preserving…

We introduce a score-based generative sampling method for solving the nonlinear filtering problem with robust accuracy. A major drawback of existing nonlinear filtering methods, e.g., particle filters, is the low stability. To overcome this…

Despite the versatility of generalized linear mixed models in handling complex experimental designs, they often suffer from misspecification and convergence problems. This makes inference on the values of coefficients problematic. To…