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We develop a framework for estimating unknown partial differential equations from noisy data, using a deep learning approach. Given noisy samples of a solution to an unknown PDE, our method interpolates the samples using a neural network,…

In this paper, conditional denoising diffusion probabilistic models (DDPMs) are proposed to enhance the data transmission and reconstruction over wireless channels. The underlying mechanism of DDPM is to decompose the data generation…

Generative models for quantum data pose significant challenges but hold immense potential in fields such as chemoinformatics and quantum physics. Quantum denoising diffusion probabilistic models (QuDDPMs) enable efficient learning of…

In this work, we address the challenge of multi-task image generation with limited data for denoising diffusion probabilistic models (DDPM), a class of generative models that produce high-quality images by reversing a noisy diffusion…

Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and…

Denoising Diffusion Probabilistic Models (DDPMs) are powerful generative deep learning models that have been very successful at image generation, and, very recently, in path planning and control. In this paper, we investigate how to…

We explore a data-driven approach for learning to optimize neural networks. We construct a dataset of neural network checkpoints and train a generative model on the parameters. In particular, our model is a conditional diffusion transformer…

The traffic matrix estimation (TME) problem has been widely researched for decades of years. Recent progresses in deep generative models offer new opportunities to tackle TME problems in a more advanced way. In this paper, we leverage the…

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…

Learning probabilistic models that can estimate the density of a given set of samples, and generate samples from that density, is one of the fundamental challenges in unsupervised machine learning. We introduce a new generative model based…

Denoising diffusion probabilistic models (DDPMs) are a recent family of generative models that achieve state-of-the-art results. In order to obtain class-conditional generation, it was suggested to guide the diffusion process by gradients…

Solving partial differential equations (PDEs) on fine spatio-temporal scales for high-fidelity solutions is critical for numerous scientific breakthroughs. Yet, this process can be prohibitively expensive, owing to the inherent complexities…

Diffusion probabilistic models (DPMs), widely recognized for their potential to generate high-quality samples, tend to go unnoticed in representation learning. While recent progress has highlighted their potential for capturing visual…

We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…

Many data-driven modules in smart grid rely on access to high-quality power flow data; however, real-world data are often limited due to privacy and operational constraints. This paper presents a physics-informed generative framework based…

Diffusion Probabilistic Models stand as a critical tool in generative modelling, enabling the generation of complex data distributions. This family of generative models yields record-breaking performance in tasks such as image synthesis,…

This work explores the theoretical and practical foundations of denoising diffusion probabilistic models (DDPMs) and score-based generative models, which leverage stochastic processes and Brownian motion to model complex data distributions.…

The vast applications of deep generative models are anchored in three core capabilities -- generating new instances, reconstructing inputs, and learning compact representations -- across various data types, such as discrete text/protein…

Data driven discovery of partial differential equations (PDEs) is a promising approach for uncovering the underlying laws governing complex systems. However, purely data driven techniques face the dilemma of balancing search space with…

Diffusion Probabilistic Models (DPMs) have emerged as the de facto approach for high-fidelity image synthesis, operating diffusion processes on continuous VAE latent, which significantly differ from the text generation methods employed by…