Memorization and Regularization in Generative Diffusion Models

Diffusion models have emerged as a powerful framework for generative modeling. At the heart of the methodology is score matching: learning gradients of families of log-densities for noisy versions of the data distribution at different scales. When the loss function adopted in score matching is evaluated using empirical data, rather than the population loss, the minimizer corresponds to the score of a time-dependent Gaussian mixture. However, use of this analytically tractable minimizer leads to data memorization: in both unconditioned and conditioned settings, the generative model returns the training samples. This paper contains an analysis of the dynamical mechanism underlying memorization. The analysis highlights the need for regularization to avoid reproducing the analytically tractable minimizer; and, in so doing, lays the foundations for a principled understanding of how to regularize. Numerical experiments investigate the properties of: (i) Tikhonov regularization; (ii) regularization designed to promote asymptotic consistency; and (iii) regularizations induced by under-parameterization of a neural network or by early stopping when training a neural network. These experiments are evaluated in the context of memorization, and directions for future development of regularization are highlighted.

Diffusion Models for Generating Ballistic Spacecraft Trajectories

Generative modeling has drawn much attention in creative and scientific data generation tasks. Score-based Diffusion Models, a type of generative model that iteratively learns to denoise data, have shown state-of-the-art results on tasks such as image generation, multivariate time series forecasting, and robotic trajectory planning. Using score-based diffusion models, this work implements a novel generative framework to generate ballistic transfers from Earth to Mars. We further analyze the model's ability to learn the characteristics of the original dataset and its ability to produce transfers that follow the underlying dynamics. Ablation studies were conducted to determine how model performance varies with model size and trajectory temporal resolution. In addition, a performance benchmark is designed to assess the generative model's usefulness for trajectory design, conduct model performance comparisons, and lay the groundwork for evaluating different generative models for trajectory design beyond diffusion. The results of this analysis showcase several useful properties of diffusion models that, when taken together, can enable a future system for generative trajectory design powered by diffusion models.

Generative Algorithms for Fusion of Physics-Based Wildfire Spread Models with Satellite Data for Initializing Wildfire Forecasts

Increases in wildfire activity and the resulting impacts have prompted the development of high-resolution wildfire behavior models for forecasting fire spread. Recent progress in using satellites to detect fire locations further provides the opportunity to use measurements to improve fire spread forecasts from numerical models through data assimilation. This work develops a method for inferring the history of a wildfire from satellite measurements, providing the necessary information to initialize coupled atmosphere-wildfire models from a measured wildfire state in a physics-informed approach. The fire arrival time, which is the time the fire reaches a given spatial location, acts as a succinct representation of the history of a wildfire. In this work, a conditional Wasserstein Generative Adversarial Network (cWGAN), trained with WRF-SFIRE simulations, is used to infer the fire arrival time from satellite active fire data. The cWGAN is used to produce samples of likely fire arrival times from the conditional distribution of arrival times given satellite active fire detections. Samples produced by the cWGAN are further used to assess the uncertainty of predictions. The cWGAN is tested on four California wildfires occurring between 2020 and 2022, and predictions for fire extent are compared against high resolution airborne infrared measurements. Further, the predicted ignition times are compared with reported ignition times. An average Sorensen's coefficient of 0.81 for the fire perimeters and an average ignition time error of 32 minutes suggest that the method is highly accurate.

Benchmarking features from different radiomics toolkits / toolboxes using Image Biomarkers Standardization Initiative

There is no consensus regarding the radiomic feature terminology, the underlying mathematics, or their implementation. This creates a scenario where features extracted using different toolboxes could not be used to build or validate the same model leading to a non-generalization of radiomic results. In this study, the image biomarker standardization initiative (IBSI) established phantom and benchmark values were used to compare the variation of the radiomic features while using 6 publicly available software programs and 1 in-house radiomics pipeline. All IBSI-standardized features (11 classes, 173 in total) were extracted. The relative differences between the extracted feature values from the different software and the IBSI benchmark values were calculated to measure the inter-software agreement. To better understand the variations, features are further grouped into 3 categories according to their properties: 1) morphology, 2) statistic/histogram and 3)texture features. While a good agreement was observed for a majority of radiomics features across the various programs, relatively poor agreement was observed for morphology features. Significant differences were also found in programs that use different gray level discretization approaches. Since these programs do not include all IBSI features, the level of quantitative assessment for each category was analyzed using Venn and the UpSet diagrams and also quantified using two ad hoc metrics. Morphology features earns lowest scores for both metrics, indicating that morphological features are not consistently evaluated among software programs. We conclude that radiomic features calculated using different software programs may not be identical and reliable. Further studies are needed to standardize the workflow of radiomic feature extraction.