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In practice functional data are sampled on a discrete set of observation points and often susceptible to noise. We consider in this paper the setting where such data are used as explanatory variables in a regression problem. If the primary…
Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each…
Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underlying noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with…
Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state…
Representation learning is all about discovering the hidden modular attributes that generate the data faithfully. We explore the potential of Denoising Diffusion Probabilistic Model (DM) in unsupervised learning of the modular attributes.…
Diffusion Probabilistic Models (DPMs) are powerful generative models that have achieved unparalleled success in a number of generative tasks. In this work, we aim to build inductive biases into the training and sampling of diffusion models…
A novel method for noise reduction in the setting of curve time series with error contamination is proposed, based on extending the framework of functional principal component analysis (FPCA). We employ the underlying, finite-dimensional…
Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models,…
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…
Sound Event Detection (SED) aims to predict the temporal boundaries of all the events of interest and their class labels, given an unconstrained audio sample. Taking either the splitand-classify (i.e., frame-level) strategy or the more…
Diffusion models have demonstrated remarkable performance in generation tasks. Nevertheless, explaining the diffusion process remains challenging due to it being a sequence of denoising noisy images that are difficult for experts to…
Denoising diffusion models are a novel class of generative algorithms that achieve state-of-the-art performance across a range of domains, including image generation and text-to-image tasks. Building on this success, diffusion models have…
Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…
Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e.,…
Diffusion generative models transform noise into data by inverting a process that progressively adds noise to data samples. Inspired by concepts from the renormalization group in physics, which analyzes systems across different scales, we…
Diffusion models generate high-dimensional data such as images by learning a process that gradually removes noise from corrupted data. Recent studies have shown that the backward dynamics of diffusion models exhibit two characteristic…
Most of the existing diffusion models use Gaussian noise for training and sampling across all time steps, which may not optimally account for the frequency contents reconstructed by the denoising network. Despite the diverse applications of…
Diffusion models have achieved state-of-the-art synthesis quality on both visual and audio tasks, and recent works further adapt them to textual data by diffusing on the embedding space. In this paper, we conduct systematic studies of the…
Diffusion models have recently exhibited remarkable abilities to synthesize striking image samples since the introduction of denoising diffusion probabilistic models (DDPMs). Their key idea is to disrupt images into noise through a fixed…
Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…