Time series data, widely used in fields such as climate studies, finance, and healthcare, often face scarcity in rare scenarios and privacy concerns, prompting growing interest in time series synthesis. Diffusion models have shown strong potential for generating high-quality data, but challenges remain in capturing long-range dependencies and complex patterns. We propose a novel diffusion model that integrates time-domain information with rich frequency-domain features, accounting for differences in noise decay rates across frequencies. Instead of arbitrary frequency splits used in prior works, we partition components based on spectral density, model them separately within the denoising backbone, and fuse them with time-domain features. This enables effective capture of both global and local patterns, enhancing representation of high- and low-frequency information. Extensive experiments on multiple public datasets show promising performance, and analyses including long-term generation and ablation studies demonstrate the model's ability to learn and represent complex time series distributions.

Causal inference involves determining how interventions affect outcomes and explaining the underlying mechanisms, and it holds critical importance across various fields. A key assumption in causal inference is that the measured covariates form a sufficient adjustment set. However, this assumption often fails due to unobserved confounders, as confounding mechanisms are rarely fully captured by measured covariates alone. Recent research has attempted to address this challenge using variational autoencoders (VAEs), but these approaches face practical limitations, including unidentifiability and bias toward proxy variables. To overcome these issues, we propose a novel method that incorporates quantized factor identifiability into VAEs for causal effect estimation. This integration mitigates unidentifiability and reduces the dominance of proxy variables, thereby enhancing consistency and accuracy in causal inference. Extensive experiments on both simulated and real-world datasets demonstrate the robustness and effectiveness of our method, establishing a new benchmark in deep causal modeling.

Vision-language models have achieved remarkable performance across various tasks by leveraging large-scale multimodal training data. However, their ability to generalize to out-of-distribution (OOD) domains requiring expert-level knowledge remains an open challenge. To address this, we investigate cross-domain transfer learning approaches for efficiently adapting diffusion classifiers to new target domains demanding expert-level domain knowledge. Specifically, we propose ExpertDiff, a head-less model reprogramming technique that optimizes the instruction-following abilities of text-to-image diffusion models via learnable prompts, while leveraging the diffusion classifier objective as a modular plug-and-play adaptor. Our approach eliminates the need for conventional output mapping layers (e.g., linear probes), enabling seamless integration with off-the-shelf diffusion frameworks like Stable Diffusion. We demonstrate the effectiveness of ExpertDiff on the various OOD datasets (i.e., medical and satellite imagery). Furthermore, we qualitatively showcase ExpertDiff’s ability to faithfully reconstruct input images, highlighting its potential for both downstream discriminative and upstream generative tasks. Our work paves the way for effectively repurposing powerful foundation models for novel OOD applications requiring domain expertise.

Alzheimer's disease (AD) is a devastating neurodegenerative condition that precedes progressive and irreversible dementia; thus, predicting its progression over time is vital for clinical diagnosis and treatment. For this, numerous studies have implemented structural magnetic resonance imaging (MRI) to model AD progression, focusing on three integral aspects: 1) temporal variability; 2) incomplete observations; and 3) temporal geometric characteristics. However, many pioneer deep learning-based approaches addressing data variability and sparsity have yet to consider inherent geometrical properties sufficiently. These properties are integral to modeling as they correlate with brain region size, thickness, volume, and shape in AD progression. The ordinary differential equation-based geometric modeling method (ODE-RGRU) has recently emerged as a promising strategy for modeling time-series data by intertwining a recurrent neural network (RNN) and an ODE in Riemannian space. Despite its achievements, ODE-RGRU encounters limitations when extrapolating positive definite symmetric matrices from incomplete samples, leading to feature reverse occurrences that are particularly problematic, especially within the clinical facet. Therefore, this study proposes a novel geometric learning approach that models longitudinal MRI biomarkers and cognitive scores by combining three modules: topological space shift, ODE-RGRU, and trajectory estimation. We have also developed a training algorithm that integrates the manifold mapping with monotonicity constraints to reflect measurement transition irreversibility. We verify our proposed method's efficacy by predicting clinical labels and cognitive scores over time in regular and irregular settings. Furthermore, we thoroughly analyze our proposed framework through an ablation study.

Alzheimer’s disease (AD) is widely aware as a neurodegenerative disease that is characterized as a leading cause of irreversible progressive dementia. From a clinical perspective, it is vital to forecast a patient’s progression over time. In that regard, there have been rigorous researches on AD progression modeling with structural magnetic resonance imaging (MRI). Methodologically, there are three major aspects of MRI modeling: (i) variability over time, (ii) sparseness in observations, and (iii) geometrical properties in temporal dynamics. While the existing deep-learning-based methods have addressed variability or sparsity in data, there is still a need to take into account the inherent geometrical properties. Recently, geometric modeling based on ordinary differential equations (ODE-RGRU) has shown its ability in various time-series data by combining an RNN and an ordinary differential equation (ODE) in symmetric positive definite (SPD) space. Despite the success of ODE-RGRU in time-series data modeling, it is limited to estimating the SPD matrix from sparse data with missing values. To this end, we propose a novel geometric learning framework for AD progression modeling to tackle the aforementioned issues simultaneously. And, we also propose training algorithms for manifold mapping on irregular and incomplete MRI and cognitive scores observations. Our proposed framework efficiently learns three major aspects of longitudinal MRI biomarker and cognitive scores by the manifold transformation module, ODE-RGRU, and missing value estimation module. We demonstrate the effectiveness of our method in experiments that forecast multi-class classification and cognitive scores over time. Additionally, we provide a multi-faceted analysis of the proposed method through an ablation study.