Search NASA⌕ Search

SEARCH · Search NASA

Results for “Diffusion models”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

CaloScore v2: single-shot calorimeter shower simulation with diffusion models

Diffusion generative models are promising alternatives for fast surrogate models, producing high-fidelity physics simulations. However, the generation time often requires an expensive denoising process with hundreds of function evaluations, restricting the current applicability of these models in a realistic setting. In this work, we report updates on the CaloScorearchitecture, detailing the changes in the diffusion process, which produces higher quality samples, and the use of progressive distillation, resulting in a diffusion model capable of generating new samples with a single function evaluation. Here we demonstrate these improvements using the Calorimeter Simulation Challenge 2022 dataset.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

DiffESM: Conditional Emulation of Temperature and Precipitation in Earth System Models With 3D Diffusion Models

Earth system models (ESMs) are essential for understanding the interaction between human activities and the Earth's climate. However, the computational demands of ESMs often limit the number of simulations that can be run, hindering the robust analysis of risks associated with extreme weather events. While low-cost climate emulators have emerged as an alternative to emulate ESMs and enable rapid analysis of future climate, many of these emulators only provide output on at most a monthly frequency. This temporal resolution is insufficient for analyzing events that require daily characterization, such as heat waves or heavy precipitation. We propose using diffusion models, a class of generative deep learning models, to effectively downscale ESM output from a monthly to a daily frequency. Trained on a handful of ESM realizations, reflecting a wide range of radiative forcings, our DiffESM model takes monthly mean precipitation or temperature as input, and is capable of producing daily values with statistical characteristics close to ESM output. Combined with a low-cost emulator providing monthly means, this approach requires only a small fraction of the computational resources needed to run a large ensemble. We evaluate model behavior using a number of extreme metrics, showing that DiffESM closely matches the spatio-temporal behavior of the ESM output it emulates in terms of the frequency and spatial characteristics of phenomena such as heat waves, dry spells, or rainfall intensity.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Modeling diffusion and types I-V sorption of water vapor in heterogeneous systems

Here, a sorption and diffusion model is developed using a mobile-immobile decomposition of the vapor concentration. Henry’s mode represents the mobile species which diffuses through the solid, while Langmuir and pooling modes represent possible immobilization processes that cause nonlinearities in sorption capacity. The model can simulate the five classical sorption types and can incorporate additional dynamics compared to models based on thermodynamic equilibrium. Additionally, the framework allows for discontinuities in material properties encountered in multi-material systems. The resulting non-linear coupled equations are solved by employing a finite element method to discretize in space, and a backward Euler method to discretize in time. The discretized system of equations is solved via a Newton-type iteration scheme at each time-step. Four different materials are parameterized for the model, which are then used in examples to demonstrate the model’s ability to capture complex sorption processes in multi-material systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Metal oxide candidates for thermochemical water splitting obtained with a generative diffusion model

Generative diffusion models (DMs) for inorganic crystalline materials are being actively investigated for their potential to expand the chemical and structural design spaces for known functional materials. Generative candidates are particularly useful for applications where few functional, let alone commercially viable, materials currently exist, such as metal oxides for thermochemical water-splitting, which have strict requirements for defect thermodynamics and host stability. Here, we critically examine generated metal oxides from the M ATTER G EN DM conditioned on select chemical systems for thermochemical water splitting applications. Perhaps most notably, we find that M ATTER G EN predicts a novel, thermodynamically stable, quinary metal oxide, Ba 2 SrInFeO 6 , although this compound represents an ordered and layered substitution within the same A 3 B 2 O 6 structural prototype as its two ternary end members. Detailed density functional theory calculations and spin configuration sampling for this material and its possible decomposition products—beyond what existed in M ATTER G EN training data—are required to quantitatively validate hull energy predictions and conclusions of stability. Furthermore, the material exhibits oxygen defect formation energies appropriate for thermochemical water splitting, warranting targeted investigation in an experimental validation campaign, along with other future M ATTER G EN candidates in this application space.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Modeling diffusion and depletion in high-aspect-ratio atomic layer deposition processes: Process parameters and manufacturing impacts

Atomic layer deposition (ALD) is a powerful technique for modifying the surface chemistry and properties of substrates with complex and nonplanar topologies. However, achieving uniform and conformal deposition on ultrahigh-aspect-ratio substrates remains challenging, typically requiring large quantities of precursors and long exposure times. Furthermore, process optimization is often performed empirically and involves substantial trial and error. In this work, we perform a combined experimental and computational study of ALD Al 2 O 3 infiltration into silica aerogel monoliths (aspect ratio >10 5 ). A reaction-diffusion model is used to explore the effects of key processing parameters, namely, exposure time per dose, precursor source temperature, number of aerogels in the reactor, and reactor volume. The model is based on quasi-static mode ALD, where the dosed precursor is held in the chamber for a fixed period of time before purging. We analyze the trade-offs between process throughput and precursor utilization for each of these parameters. Furthermore, we investigate the co-optimization and interactions between multiple process parameters, demonstrating the potential for further improvements. Furthermore, this physics-based model can be used to identify a set of process parameters for high-aspect-ratio ALD that meet specific manufacturing objective functions, including throughput, cost, and sustainability.

Aerogel↗
DOE OSTI2022

On the Importance of Using Event-Specific Wave Diffusion Rates in Modeling Diffuse Electron Precipitation

A few to tens of keV electron precipitation that carries substantial energy source down to the upper atmosphere to create aurora is manifested as an important magnetosphere-ionosphere coupling process. The precipitation is usually caused by scattering processes associated with plasma waves in the magnetosphere. The scattering process is often quantified by wave diffusion rates that indicate how fast an electron is scattered. Global models commonly use diffusion coefficients that are derived from statistical wave models. However, due to the statistical nature, many localized, transient features could be smeared out. In this study, we investigate electron precipitation using event-specific diffusion coefficients that are obtained based on simultaneous in-situ measured/inferred, rather than statistical, chorus wave dynamics. We find that the application of the event-specific diffusion coefficients associated with a more dynamic and intense chorus wave model leads more electrons, particularly at several to tens of keV in the dawn-to-noon sector at L > 3, to precipitate than using statistical coefficients. Here, the new simulation roughly captures both the intensity and variability of the precipitating flux as detected by the NOAA/POES satellites. Ionospheric electron density in the lower E region (100–120 km) observed by the mid-latitude Millstone Hill radar is also much better reproduced, while the case using statistical diffusion coefficients underestimates the ionization rate. This study implies the importance of using event-specific diffusion rates in simulating the diffuse electron precipitation and understanding the magnetosphere-ionosphere coupling.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Development of physics-consistent conditional diffusion model to overcome data scarcity in critical heat flux

Deep generative modeling provides a powerful pathway to overcome data scarcity in energy-related applications where experimental data are often limited. By learning the underlying probability distribution of the training dataset, deep generative models, such as the diffusion model, can generate high-fidelity synthetic samples that statistically resemble the training data. Such synthetic data generation can significantly enrich the size and diversity of the available training data, and more importantly, improve the robustness of downstream machine learning models in predictive tasks. The objective of this paper is to investigate the effectiveness of diffusion models for overcoming data scarcity in nuclear energy applications. By leveraging a public dataset on critical heat flux which covers a wide range of commercial nuclear reactor operational conditions, we developed a diffusion model that can generate an arbitrary amount of synthetic samples. Since a vanilla diffusion model can only generate samples randomly, we also developed a conditional diffusion model capable of generating targeted critical heat flux data under user-specified thermal-hydraulic conditions. The performance of the diffusion model was evaluated based on its ability to capture empirical feature distributions and pair-wise correlations, as well as to maintain physical consistency. The results showed that both the diffusion model and conditional diffusion model can successfully generate realistic and physics-consistent critical heat flux data. Furthermore, uncertainty quantification results demonstrate that the conditional diffusion model is highly effective in augmenting critical heat flux data while maintaining acceptable levels of uncertainty.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

FunDiff: diffusion models over function spaces for physics-informed generative modeling

Recent advances in generative modeling-particularly diffusion models and flow matching-have been widely used for synthesizing discrete data such as images and videos. However, adapting these models to physical applications remains challenging, as the quantities of interest are continuous functions governed by complex physical laws. To address this, we introduce FunDiff, an efficient and robust framework for generative modeling in function spaces. FunDiff combines a latent diffusion process with a function autoencoder architecture to handle input functions with varying discretizations, generates continuous functions that can be evaluated at arbitrary locations, and seamlessly incorporate physical priors. These priors are enforced through architectural constraints or physics-informed loss functions, ensuring that generated samples satisfy fundamental physical laws. We theoretically establish minimax optimality guarantees for density estimation in function spaces, demonstrating that diffusion-based estimators achieve optimal convergence rates under suitable regularity conditions. We further demonstrate the practical effectiveness of FunDiff across diverse applications in fluid dynamics and solid mechanics. Empirical results indicate that our method can generate physically consistent samples with high fidelity to the target distribution, and exhibit robustness to noisy and low-resolution data.

Wang, Sifan [Yale University, New Haven, CT (Unite↗
DOE OSTI2024

Diffusion-Model-Assisted Supervised Learning of Generative Models for Density Estimation

Here, we present a supervised learning framework of training generative models for density estimation. Generative models, including generative adversarial networks (GANs), normalizing flows, and variational auto-encoders (VAEs), are usually considered as unsupervised learning models, because labeled data are usually unavailable for training. Despite the success of the generative models, there are several issues with the unsupervised training, e.g., requirement of reversible architectures, vanishing gradients, and training instability. To enable supervised learning in generative models, we utilize the score-based diffusion model to generate labeled data. Unlike existing diffusion models that train neural networks to learn the score function, we develop a training-free score estimation method. This approach uses mini-batch-based Monte Carlo estimators to directly approximate the score function at any spatial-temporal location in solving an ordinary differential equation (ODE), corresponding to the reverse-time stochastic differential equation (SDE). This approach can offer both high accuracy and substantial time savings in neural network training. Once the labeled data are generated, we can train a simple, fully connected neural network to learn the generative model in the supervised manner. Compared with existing normalizing flow models, our method does not require the use of reversible neural networks and avoids the computation of the Jacobian matrix. Compared with existing diffusion models, our method does not need to solve the reverse-time SDE to generate new samples. As a result, the sampling efficiency is significantly improved. We demonstrate the performance of our method by applying it to a set of 2D datasets as well as real data from the University of California Irvine (UCI) repository.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Random Walks With Tweedie: A Unified View of Score-Based Diffusion Models [In the Spotlight]

We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals—particularly natural images—and often play a role in state-of-the-art algorithms for inverse problems in image processing. While these algorithms are often surprisingly simple, the theory behind them is not, and multiple complex theoretical justifications exist in the literature. Here, in this study, we provide a simple and largely self-contained theoretical justification for score-based diffusion models that is targeted towards the signal processing community. This approach leads to generic algorithmic templates for training and generating samples with diffusion models. We show that several influential diffusion models correspond to particular choices within these templates and demonstrate that alternative, more straightforward algorithmic choices can provide comparable results. This approach has the added benefit of enabling conditional sampling without any likelihood approximation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Experimental observation of nonlinear relation between pressure and water flux is consistent with the solution-diffusion model

In several recent studies, it has been proposed that the fundamental understanding of penetrant transport in dense polymer membranes occurring via the solution-diffusion model, which has been the generally accepted theoretical framework for describing penetrant transport in such materials for the past several decades, is flawed. An alternate mechanistic framework based on the idea of two-phase flow in a porous medium (i.e., pore-flow) has been broadly advanced instead, with proponents of this approach claiming that the pore-flow theoretical framework provides the necessary mechanistic insight to design novel polymeric membrane materials for emerging applications. In this study, we show experimental results for hydraulic permeation of water that are entirely consistent with the solution-diffusion theory, without modification, for three dense polymeric membranes: crosslinked poly(ethylene glycol diacrylate) (XLPEGDA), Nafion 117 ionomer in the sodium counterion form (Nafion 117-Na), and cellulose acetate (CA). By measuring water flux at transmembrane pressures up to 240 bar, we observe a nonlinear relationship between the transmembrane pressure (TMP) and water flux, J w , for XLPEGDA and Nafion 117-Na, while this relationship is linear for CA. We demonstrate that the behavior of these three materials is described via the solution-diffusion model. According to the solution-diffusion model, flux is, to a good approximation, proportional to the transmembrane concentration difference induced by the pressure difference across the membrane, rather than to TMP itself. Water sorption isotherms are reported for all three materials. They further justify the nonlinear relationship between TMP and J w observed in XLPEGDA and Nafion 117-Na, emphasizing that the nonlinearity in the flux/TMP relationship stems from nonlinearities in the sorption isotherm with pressure. Additionally, the relationship between water flux and TMP can be predicted, a priori, with no adjustable parameters when a predictive model for the diffusion coefficient of water is employed in conjunction with the experimental water sorption isotherms in the solution-diffusion model. Furthermore, our results demonstrate the validity of the solution-diffusion model to describe transport of penetrants in dense polymer membranes, while highlighting the sensitivity of the solution-diffusion model to the many physical and mathematical simplifications commonly applied to the theory in literature.

materials↗
DOE OSTI2025

Modeling inter‐reader variability in clinical target volume delineation for soft tissue sarcomas using diffusion model

Abstract Background Accurate delineation of the clinical target volume (CTV) is essential in the radiotherapy treatment of soft tissue sarcomas. However, this process is subject to inter‐reader variability due to the need for clinical assessment of risk and extent of potential microscopic spread. This can lead to inconsistencies in treatment planning, potentially impacting treatment outcomes. Most existing automatic CTV delineation methods do not account for this variability and can only generate a single CTV for each case. Purpose This study aims to develop a deep learning‐based technique to generate multiple CTV contours for each case, simulating the inter‐reader variability in the clinical practice. Methods We employed a publicly available dataset consisting of fluorodeoxyglucose positron emission tomography (FDG‐PET), x‐ray computed tomography (CT), and pre‐contrast T1‐weighted magnetic resonance imaging (MRI) scans from 51 patients with soft tissue sarcoma, along with an independent validation set containing five additional patients. An experienced reader drew a contour of the gross tumor volume (GTV) for each patient based on multi‐modality images. Subsequently, two additional readers, together with the first one, were responsible for contouring three CTVs in total based on the GTV. We developed a diffusion model‐based deep learning method that is capable of generating arbitrary number of different and plausible CTVs to mimic the inter‐reader variability in CTV delineation. The proposed model incorporates a separate encoder to extract features from the GTV masks, leveraging the critical role of GTV information in accurate CTV delineation. Results The proposed diffusion model demonstrated superior performance with the highest Dice Index (0.902 compared to values below 0.881 for state‐of‐the‐art models) and the best generalized energy distance (GED) (0.209 compared to values exceeding 0.221 for state‐of‐the‐art models). It also achieved the second‐highest recall and precision metrics among the compared ambiguous image segmentation models. Results from both datasets exhibited consistent trends, reinforcing the reliability of our findings. Additionally, ablation studies exploring different model structures and input configurations highlighted the significance of incorporating prior GTV information for accurate CTV delineation. Conclusions The proposed diffusion model successfully generates multiple plausible CTV contours for soft tissue sarcomas, effectively capturing inter‐reader variability in CTV delineation.

Dong, Yafei [Yale Biomedical Imaging Institute Yal↗
DOE OSTI2023

Ensemble flow reconstruction in the atmospheric boundary layer from spatially limited measurements through latent diffusion models

Due to costs and practical constraints, field campaigns in the atmospheric boundary layer typically only measure a fraction of the atmospheric volume of interest. Machine learning techniques have previously successfully reconstructed unobserved regions of flow in canonical fluid mechanics problems and two-dimensional geophysical flows, but these techniques have not yet been demonstrated in the three-dimensional atmospheric boundary layer. Here, we conduct a numerical analogue of a field campaign with spatially limited measurements using large-eddy simulation. We pose flow reconstruction as an inpainting problem, and reconstruct realistic samples of turbulent, three-dimensional flow with the use of a latent diffusion model. The diffusion model generates physically plausible turbulent structures on larger spatial scales, even when input observations cover less than 1% of the volume. Through a combination of qualitative visualization and quantitative assessment, we demonstrate that the diffusion model generates meaningfully diverse samples when conditioned on just one observation. These samples successfully serve as initial conditions for a large-eddy simulation code. We find that diffusion models show promise and potential for other applications for other turbulent flow reconstruction problems.

17 WIND ENERGY↗
DOE OSTI2023

Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces

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 spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion as well as other approaches to discrete diffusion, and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce “Blackout Diffusion”, which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.

Santos, Javier E.↗
DOE OSTI2023

Code for the manuscript titled "Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces"

We would like to disclose two scripts, written in Jupyter notebook, in which we implement the "Blackout Diffusion Process" described in the manuscript "Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces" (LA-UR-23-20509), to be submitted to the International Conference of Machine Learning (ICML). The abstract of the manuscript is append below. == Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, which occur in many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process. We relate the theory to the existing continuous-state Gaussian diffusion and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce "Blackout Diffusion", which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10 dataset confirm the feasibility of generative diffusion modeling in a discrete space. Generalizing from specific (Gaussian) forward processes to a more general framework also sheds light on how to interpret generative diffusion models and their mathematical structure, which we comment on.

Lin, Yen Ting↗
DOE OSTI2026

Multi-Objective design of interlocking metasurfaces using conditional diffusion models

Unit cell design remains a major challenge for interlocking metasurfaces, a promising joining technology for dissimilar materials, due to the complex, competing, multivariate design space and the need for rapid adaptation to varying performance requirements. This study explores Conditional Diffusion Models as a design optimization tool for interlocking metasurfaces. Given the complex, competing, multivariate design space for interlocking metasurfaces, unit cell design remains a major challenge for this joining technology. We trained a conditional diffusion model on 25,000 finite element analysis-simulated interlocking metasurface unit cells to generate designs with tailored thermo-mechanical properties (tensile strength, shear strength, and thermal conductivity) based on specified performance criteria. The model demonstrated a success rate of approximately 72 % in producing designs that met specified property bounds. The conditional diffusion model generated both thermally resistive and conductive designs, revealing clear trends in design characteristics: taller, dendritic structures were advantageous for tensile loads, while shorter, robust designs excelled in shear applications. Our findings indicate that the model's performance is more influenced by the breadth of the design space than by the quantity of training data, highlighting the importance of expansive design domains for generating innovative solutions. This work establishes conditional diffusion models as a highly efficient and adaptable tool for rapid interlocking metasurface unit cell design, paving the way for advancements in multi-material joining technologies, as well as highlighting the justification to leverage conditional diffusion models as design tools across complex design domains.

Conditional diffusion models↗
DOE OSTI2023

Accelerating Markov Chain Monte Carlo sampling with diffusion models

Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a Metropolis-Hastings algorithm with a diffusion model that can draw global samples with the aim of approximating the posterior. We briefly review diffusion models in the context of image synthesis before providing a streamlined diffusion model tailored towards low-dimensional data arrays. We then present our adapted Metropolis-Hastings algorithm which combines local proposals with global proposals taken from a diffusion model that is regularly trained on the samples produced during the MCMC run. Our approach leads to a significant reduction in the number of likelihood evaluations required to obtain an accurate representation of the Bayesian posterior across several analytic functions, as well as for a physical example based on a global fit of parton distribution functions. Our method is extensible to other MCMC techniques, and we briefly compare our method to similar approaches based on normalising flows. A code implementation can be found at https://github.com/NickHunt-Smith/MCMC-diffusion.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗