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A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

Machine Learning · Computer Science 2025-04-22 Dimitris G. Giovanis , Ellis Crabtree , Roger G. Ghanem , Ioannis G. Kevrekidis

The design of aerodynamic shapes, such as airfoils, has traditionally required significant computational resources and relied on predefined design parameters, which limit the potential for novel shape synthesis. In this work, we introduce a…

Machine Learning · Computer Science 2024-12-19 Reid Graves , Amir Barati Farimani

Acquiring high-quality data for training discriminative models is a crucial yet challenging aspect of building effective predictive systems. In this paper, we present Diffusion Inversion, a simple yet effective method that leverages the…

Computer Vision and Pattern Recognition · Computer Science 2023-05-25 Yongchao Zhou , Hshmat Sahak , Jimmy Ba

Learning a categorical distribution comes with its own set of challenges. A successful approach taken by state-of-the-art works is to cast the problem in a continuous domain to take advantage of the impressive performance of the generative…

Machine Learning · Computer Science 2023-03-09 Florence Regol , Mark Coates

Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…

Machine Learning · Computer Science 2023-05-02 Lequan Lin , Zhengkun Li , Ruikun Li , Xuliang Li , Junbin Gao

Synthesizing fully developed three-dimensional turbulent velocity fields remains a long-standing problem in fluid mechanics and an open challenge for generative modeling. The difficulty arises from the coexistence of extreme dimensionality,…

Fluid Dynamics · Physics 2026-03-16 Tianyi Li , Michele Buzzicotti , Fabio Bonaccorso , Luca Biferale

In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…

Fluid Dynamics · Physics 2025-07-14 Yannick Gachnang , Vismay Churiwala

Turbulent flows have historically presented formidable challenges to predictive computational modeling. Traditional numerical simulations often require vast computational resources, making them infeasible for numerous engineering…

Fluid Dynamics · Physics 2023-11-15 Han Gao , Xu Han , Xiantao Fan , Luning Sun , Li-Ping Liu , Lian Duan , Jian-Xun Wang

The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…

Fluid Dynamics · Physics 2026-01-09 Marc Amorós-Trepat , Luis Medrano-Navarro , Qiang Liu , Luca Guastoni , Nils Thuerey

We provide an overview of the diffusion model as a method to generate new samples. Generative models have been recently adopted for tasks such as art generation (Stable Diffusion, Dall-E) and text generation (ChatGPT). Diffusion models in…

Machine Learning · Statistics 2025-06-13 Justin Le

Seismic imaging from sparsely acquired data faces challenges such as low image quality, discontinuities, and migration swing artifacts. Existing convolutional neural network (CNN)-based methods struggle with complex feature distributions…

Geophysics · Physics 2024-08-01 Xingchen Shi , Shijun Cheng , Weijian Mao , Wei Ouyang

Diffusion models have attained prominence for their ability to synthesize a probability distribution for a given dataset via a diffusion process, enabling the generation of new data points with high fidelity. However, diffusion processes…

Machine Learning · Computer Science 2024-11-25 Shervin Khalafi , Dongsheng Ding , Alejandro Ribeiro

Learning-based models for fluid dynamics often operate in unconstrained function spaces, leading to physically inadmissible, unstable simulations. While penalty-based methods offer soft regularization, they provide no structural guarantees,…

Machine Learning · Computer Science 2026-03-26 Xigui Li , Hongwei Zhang , Ruoxi Jiang , Deshu Chen , Chensen Lin , Limei Han , Yuan Qi , Xin Guo , Yuan Cheng

Computer-assisted interventions can improve intra-operative guidance, particularly through deep learning methods that harness the spatiotemporal information in surgical videos. However, the severe data imbalance often found in surgical…

Computer Vision and Pattern Recognition · Computer Science 2025-05-16 Danush Kumar Venkatesh , Isabel Funke , Micha Pfeiffer , Fiona Kolbinger , Hanna Maria Schmeiser , Juergen Weitz , Marius Distler , Stefanie Speidel

Diffusion models have demonstrated remarkable performance in generating unimodal data across various tasks, including image, video, and text generation. On the contrary, the joint generation of multimodal data through diffusion models is…

Machine Learning · Computer Science 2025-06-16 Kevin Rojas , Yuchen Zhu , Sichen Zhu , Felix X. -F. Ye , Molei Tao

Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…

Numerical Analysis · Mathematics 2024-11-08 Alexander Lobbe , Dan Crisan , Oana Lang

We tackle the problem of sampling from intractable high-dimensional density functions, a fundamental task that often appears in machine learning and statistics. We extend recent sampling-based approaches that leverage controlled stochastic…

Machine Learning · Computer Science 2024-03-12 Dinghuai Zhang , Ricky T. Q. Chen , Cheng-Hao Liu , Aaron Courville , Yoshua Bengio

Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusion models are repurposed for solving inverse problems using…

Recent advances in generative artificial intelligence have enabled the creation of high-quality synthetic data that closely mimics real-world data. This paper explores the adaptation of the Stable Diffusion 2.0 model for generating…

Machine Learning · Computer Science 2024-05-07 Eugenio Lomurno , Matteo D'Oria , Matteo Matteucci

Next-generation galaxy surveys promise unprecedented precision in testing gravity at cosmological scales. However, realising this potential requires accurately modelling the non-linear cosmic web. We address this challenge by exploring…

Cosmology and Nongalactic Astrophysics · Physics 2025-08-20 Julieth Katherine Riveros , Paola Saavedra , Hector J. Hortua , Jorge Enrique Garcia-Farieta , Ivan Olier