Unraveling the Temporal Dynamics of the Unet in Diffusion Models

Diffusion models have garnered significant attention since they can effectively learn complex multivariate Gaussian distributions, resulting in diverse, high-quality outcomes. They introduce Gaussian noise into training data and reconstruct the original data iteratively. Central to this iterative process is a single Unet, adapting across time steps to facilitate generation. Recent work revealed the presence of composition and denoising phases in this generation process, raising questions about the Unets' varying roles. Our study dives into the dynamic behavior of Unets within denoising diffusion probabilistic models (DDPM), focusing on (de)convolutional blocks and skip connections across time steps. We propose an analytical method to systematically assess the impact of time steps and core Unet components on the final output. This method eliminates components to study causal relations and investigate their influence on output changes. The main purpose is to understand the temporal dynamics and identify potential shortcuts during inference. Our findings provide valuable insights into the various generation phases during inference and shed light on the Unets' usage patterns across these phases. Leveraging these insights, we identify redundancies in GLIDE (an improved DDPM) and improve inference time by ~27% with minimal degradation in output quality. Our ultimate goal is to guide more informed optimization strategies for inference and influence new model designs.

Class-constrained t-SNE: Combining Data Features and Class Probabilities

Data features and class probabilities are two main perspectives when, e.g., evaluating model results and identifying problematic items. Class probabilities represent the likelihood that each instance belongs to a particular class, which can be produced by probabilistic classifiers or even human labeling with uncertainty. Since both perspectives are multi-dimensional data, dimensionality reduction (DR) techniques are commonly used to extract informative characteristics from them. However, existing methods either focus solely on the data feature perspective or rely on class probability estimates to guide the DR process. In contrast to previous work where separate views are linked to conduct the analysis, we propose a novel approach, class-constrained t-SNE, that combines data features and class probabilities in the same DR result. Specifically, we combine them by balancing two corresponding components in a cost function to optimize the positions of data points and iconic representation of classes -- class landmarks. Furthermore, an interactive user-adjustable parameter balances these two components so that users can focus on the weighted perspectives of interest and also empowers a smooth visual transition between varying perspectives to preserve the mental map. We illustrate its application potential in model evaluation and visual-interactive labeling. A comparative analysis is performed to evaluate the DR results.

Neural Spherical Harmonics for structurally coherent continuous representation of diffusion MRI signal

We present a novel way to model diffusion magnetic resonance imaging (dMRI) datasets, that benefits from the structural coherence of the human brain while only using data from a single subject. Current methods model the dMRI signal in individual voxels, disregarding the intervoxel coherence that is present. We use a neural network to parameterize a spherical harmonics series (NeSH) to represent the dMRI signal of a single subject from the Human Connectome Project dataset, continuous in both the angular and spatial domain. The reconstructed dMRI signal using this method shows a more structurally coherent representation of the data. Noise in gradient images is removed and the fiber orientation distribution functions show a smooth change in direction along a fiber tract. We showcase how the reconstruction can be used to calculate mean diffusivity, fractional anisotropy, and total apparent fiber density. These results can be achieved with a single model architecture, tuning only one hyperparameter. In this paper we also demonstrate how upsampling in both the angular and spatial domain yields reconstructions that are on par or better than existing methods.

Incorporating Texture Information into Dimensionality Reduction for High-Dimensional Images

High-dimensional imaging is becoming increasingly relevant in many fields from astronomy and cultural heritage to systems biology. Visual exploration of such high-dimensional data is commonly facilitated by dimensionality reduction. However, common dimensionality reduction methods do not include spatial information present in images, such as local texture features, into the construction of low-dimensional embeddings. Consequently, exploration of such data is typically split into a step focusing on the attribute space followed by a step focusing on spatial information, or vice versa. In this paper, we present a method for incorporating spatial neighborhood information into distance-based dimensionality reduction methods, such as t-Distributed Stochastic Neighbor Embedding (t-SNE). We achieve this by modifying the distance measure between high-dimensional attribute vectors associated with each pixel such that it takes the pixel's spatial neighborhood into account. Based on a classification of different methods for comparing image patches, we explore a number of different approaches. We compare these approaches from a theoretical and experimental point of view. Finally, we illustrate the value of the proposed methods by qualitative and quantitative evaluation on synthetic data and two real-world use cases.

Linear tSNE optimization for the Web

The t-distributed Stochastic Neighbor Embedding (tSNE) algorithm has become in recent years one of the most used and insightful techniques for the exploratory data analysis of high-dimensional data. tSNE reveals clusters of high-dimensional data points at different scales while it requires only minimal tuning of its parameters. Despite these advantages, the computational complexity of the algorithm limits its application to relatively small datasets. To address this problem, several evolutions of tSNE have been developed in recent years, mainly focusing on the scalability of the similarity computations between data points. However, these contributions are insufficient to achieve interactive rates when visualizing the evolution of the tSNE embedding for large datasets. In this work, we present a novel approach to the minimization of the tSNE objective function that heavily relies on modern graphics hardware and has linear computational complexity. Our technique does not only beat the state of the art, but can even be executed on the client side in a browser. We propose to approximate the repulsion forces between data points using adaptive-resolution textures that are drawn at every iteration with WebGL. This approximation allows us to reformulate the tSNE minimization problem as a series of tensor operation that are computed with TensorFlow.js, a JavaScript library for scalable tensor computations.

Approximated and User Steerable tSNE for Progressive Visual Analytics

Progressive Visual Analytics aims at improving the interactivity in existing analytics techniques by means of visualization as well as interaction with intermediate results. One key method for data analysis is dimensionality reduction, for example, to produce 2D embeddings that can be visualized and analyzed efficiently. t-Distributed Stochastic Neighbor Embedding (tSNE) is a well-suited technique for the visualization of several high-dimensional data. tSNE can create meaningful intermediate results but suffers from a slow initialization that constrains its application in Progressive Visual Analytics. We introduce a controllable tSNE approximation (A-tSNE), which trades off speed and accuracy, to enable interactive data exploration. We offer real-time visualization techniques, including a density-based solution and a Magic Lens to inspect the degree of approximation. With this feedback, the user can decide on local refinements and steer the approximation level during the analysis. We demonstrate our technique with several datasets, in a real-world research scenario and for the real-time analysis of high-dimensional streams to illustrate its effectiveness for interactive data analysis.

Fuzzy Fibers: Uncertainty in dMRI Tractography

Fiber tracking based on diffusion weighted Magnetic Resonance Imaging (dMRI) allows for noninvasive reconstruction of fiber bundles in the human brain. In this chapter, we discuss sources of error and uncertainty in this technique, and review strategies that afford a more reliable interpretation of the results. This includes methods for computing and rendering probabilistic tractograms, which estimate precision in the face of measurement noise and artifacts. However, we also address aspects that have received less attention so far, such as model selection, partial voluming, and the impact of parameters, both in preprocessing and in fiber tracking itself. We conclude by giving impulses for future research.

Visual Exploration of Simulated and Measured Blood Flow

Morphology of cardiovascular tissue is influenced by the unsteady behavior of the blood flow and vice versa. Therefore, the pathogenesis of several cardiovascular diseases is directly affected by the blood-flow dynamics. Understanding flow behavior is of vital importance to understand the cardiovascular system and potentially harbors a considerable value for both diagnosis and risk assessment. The analysis of hemodynamic characteristics involves qualitative and quantitative inspection of the blood-flow field. Visualization plays an important role in the qualitative exploration, as well as the definition of relevant quantitative measures and its validation. There are two main approaches to obtain information about the blood flow: simulation by computational fluid dynamics, and in-vivo measurements. Although research on blood flow simulation has been performed for decades, many open problems remain concerning accuracy and patient-specific solutions. Possibilities for real measurement of blood flow have recently increased considerably by new developments in magnetic resonance imaging which enable the acquisition of 3D quantitative measurements of blood-flow velocity fields. This chapter presents the visualization challenges for both simulation and real measurements of unsteady blood-flow fields.