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Medical image segmentation is a challenging task, made more difficult by many datasets' limited size and annotations. Denoising diffusion probabilistic models (DDPM) have recently shown promise in modelling the distribution of natural…
Denoising Diffusion Probabilistic Models (DDPMs) have gained great attention in adversarial purification. Current diffusion-based works focus on designing effective condition-guided mechanisms while ignoring a fundamental problem, i.e., the…
Denoising Diffusion Probabilistic Model (DDPM) is able to make flexible conditional image generation from prior noise to real data, by introducing an independent noise-aware classifier to provide conditional gradient guidance at each time…
In the context of nonparametric Bayesian estimation a Markov chain Monte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional…
Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not…
This paper concerns the mathematical analyses of the diffusion model in machine learning. The drift term of the backward sampling process is represented as a conditional expectation involving the data distribution and the forward diffusion.…
Generative modeling of non-negative, discrete data, such as symbolic music, remains challenging due to two persistent limitations in existing methods. Firstly, many approaches rely on modeling continuous embeddings, which is suboptimal for…
In Diffusion Probabilistic Models (DPMs), the task of modeling the score evolution via a single time-dependent neural network necessitates extended training periods and may potentially impede modeling flexibility and capacity. To counteract…
Discrete diffusion models are a powerful class of generative models with strong performance across many domains. For efficiency, however, discrete diffusion typically parameterizes the generative (reverse) process with factorized…
Denoising diffusion probabilistic models (DDPMs) have emerged as powerful generative models for complex distributions, yet their use in arbitrage-free derivative pricing remains largely unexplored. Financial asset prices are naturally…
Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…
Discrete diffusion has recently emerged as a promising paradigm in discrete data modeling. However, existing methods typically rely on a fixed rate transition matrix during training, which not only limits the expressiveness of latent…
We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…
Diffusion Probabilistic Models (DPMs) have achieved great success in image generation but suffer from high inference latency due to their iterative denoising nature. Motivated by the evolving feature dynamics across the denoising…
In recent advancements in high-fidelity image generation, Denoising Diffusion Probabilistic Models (DDPMs) have emerged as a key player. However, their application at high resolutions presents significant computational challenges. Current…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
Through Diffusion Models (DMs), we have made significant advances in generating high-quality images. Our exploration of these models delves deeply into their core operational principles by systematically investigating key aspects across…
Distribution matching (DM) is a versatile domain-invariant representation learning technique that has been applied to tasks such as fair classification, domain adaptation, and domain translation. Non-parametric DM methods struggle with…
Denoising Diffusion Probabilistic Models (DDPMs) have emerged as a powerful family of generative models that can yield high-fidelity samples and competitive log-likelihoods across a range of domains, including image and speech synthesis.…
Diffusion models have quickly become some of the most popular and powerful generative models for high-dimensional data. The key insight that enabled their development was the realization that access to the score -- the gradient of the…