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A common problem in Bayesian inference is the sampling of target probability distributions at sufficient resolution and accuracy to estimate the probability density, and to compute credible regions. Often by construction, many target…

We present a generative learning framework for probabilistic sampling based on an extension of the Probabilistic Learning on Manifolds (PLoM) approach, which is designed to generate statistically consistent realizations of a random vector…

Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified…

Score-based diffusion models synthesize samples by reversing a stochastic process that diffuses data to noise, and are trained by minimizing a weighted combination of score matching losses. The log-likelihood of score-based diffusion models…

Score-based generative models (SGMs) are powerful tools to sample from complex data distributions. Their underlying idea is to (i) run a forward process for time $T_1$ by adding noise to the data, (ii) estimate its score function, and (iii)…

Score-based generative models have demonstrated significant practical success in data-generating tasks. The models establish a diffusion process that perturbs the ground truth data to Gaussian noise and then learn the reverse process to…

Diffusion models have become a standard approach for generative modeling in continuous domains, yet their application to discrete data remains challenging. We investigate why Gaussian diffusion models with the DDPM solver struggle to sample…

Although continuous-time consistency models (e.g., sCM, MeanFlow) are theoretically principled and empirically powerful for fast academic-scale diffusion, its applicability to large-scale text-to-image and video tasks remains unclear due to…

This paper introduces Discrete Markov Probabilistic Models (DMPMs), a novel discrete diffusion algorithm for discrete data generation. The algorithm operates in discrete bit space, where the noising process is a continuous-time Markov chain…

Diffusion Models (DMs) have achieved great success in image generation and other fields. By fine sampling through the trajectory defined by the SDE/ODE solver based on a well-trained score model, DMs can generate remarkable high-quality…

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…

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…

We present a new methodology for detecting out-of-distribution (OOD) images by utilizing norms of the score estimates at multiple noise scales. A score is defined to be the gradient of the log density with respect to the input data. Our…

Text-to-image diffusion models pre-trained on billions of image-text pairs have recently enabled 3D content creation by optimizing a randomly initialized differentiable 3D representation with score distillation. However, the optimization…

We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…

Current 4D generation methods have achieved noteworthy efficacy with the aid of advanced diffusion generative models. However, these methods lack multi-view spatial-temporal modeling and encounter challenges in integrating diverse prior…

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion…

Score-based diffusion models generate samples from an unknown target distribution using a time-reversed diffusion process. While such models represent state-of-the-art approaches in industrial applications such as artificial image…

Under the data manifold hypothesis, high-dimensional data are concentrated near a low-dimensional manifold. We study the problem of Riemannian optimization over such manifolds when they are given only implicitly through the data…

Score distillation sampling (SDS), the methodology in which the score from pretrained 2D diffusion models is distilled into 3D representation, has recently brought significant advancements in text-to-3D generation task. However, this…