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The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…

Recently, research on denoising diffusion models has expanded its application to the field of image restoration. Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the…

Diffusion Models (DMs) have achieved state-of-the-art generative performance across multiple modalities, yet their sampling process remains prohibitively slow due to the need for hundreds of function evaluations. Recent progress in…

Rendering bridges the gap between 2D vision and 3D scenes by simulating the physical process of image formation. By inverting such renderer, one can think of a learning approach to infer 3D information from 2D images. However, standard…

Discrete diffusion models have emerged as a promising direction for vision-language tasks, offering bidirectional context modeling and theoretical parallelization. However, their practical application is severely hindered by a…

There is growing evidence that converting targets to soft targets in supervised learning can provide considerable gains in performance. Much of this work has considered classification, converting hard zero-one values to soft labels---such…

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 models have shown remarkable promise for image restoration by leveraging powerful priors. Prominent methods typically frame the restoration problem within a Bayesian inference framework, which iteratively combines a denoising step…

The Graph Edit Distance (GED) problem, which aims to compute the minimum number of edit operations required to transform one graph into another, is a fundamental challenge in graph analysis with wide-ranging applications. However, due to…

Discrete diffusion has emerged as a powerful framework for generative modeling in discrete domains, yet efficiently sampling from these models remains challenging. Existing sampling strategies often struggle to balance computation and…

Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…

Diffusion models have recently gained popularity for accelerated MRI reconstruction due to their high sample quality. They can effectively serve as rich data priors while incorporating the forward model flexibly at inference time, and they…

Generative models such as Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs) have shown promise in sequential recommendation tasks. However, they face challenges, including posterior collapse and limited…

Multi-fidelity surrogate learning is important for physical simulation related applications in that it avoids running numerical solvers from scratch, which is known to be costly, and it uses multi-fidelity examples for training and greatly…

Gradient-based approximate inference methods, such as Stein variational gradient descent (SVGD), provide simple and general-purpose inference engines for differentiable continuous distributions. However, existing forms of SVGD cannot be…

The development of diffusion-based generative models over the past decade has largely proceeded independently of progress in representation learning. These diffusion models typically rely on regression-based objectives and generally lack…

Discrete diffusion models with absorbing processes have shown promise in language modeling. The key quantities to be estimated are the ratios between the marginal probabilities of two transitive states at all timesteps, called the concrete…

Diffusion models (DMs) have made significant progress in the fields of image, audio, and video generation. One downside of DMs is their slow iterative process. Recent algorithms for fast sampling are designed from the perspective of…

Due to the high complexity and technical requirements of industrial production processes, surface defects will inevitably appear, which seriously affects the quality of products. Although existing lightweight detection networks are highly…

Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…