Time Series Generation

Fine-grained energy consumption data are essential for applications such as demand forecasting, demand response planning, and grid reliability assessment. However, access to such data is often restricted by privacy concerns and data-sharing constraints, motivating growing interest in synthetic energy data generation. Although existing methods can reproduce overall consumption distributions and recurring temporal patterns, they often smooth out or underrepresent anomalous events caused by extreme weather, infrastructure failures, and behavioral shifts. Preserving these events is challenging because they are sparse, localized in time and space, and shaped by heterogeneous dependencies across geographical proximity and regional attributes. To address these challenges, we propose SynEnergy, a two-stage diffusion-based framework for anomaly-preserving energy consumption data generation. The first stage, Heterogeneous Graph-based Anomaly Semantic Learning (HG-ASL), extracts region-specific anomaly semantics from sparse residual structures by jointly modeling spatial and attribute dependencies across urban regions. The second stage, Anomaly Semantic-guided Diffusion (AS-Diff), injects the learned anomaly semantics into the denoising process to generate realistic consumption sequences while preserving anomalous patterns. This design enables controllable generation for individual regions and scales naturally to city-wide settings. We evaluate SynEnergy on four real-world energy consumption datasets against 11 general-purpose and energy-specific generation baselines. Experimental results show that SynEnergy improves anomaly preservation fidelity by an average of 12.21% and downstream quality by 2.96%, while maintaining competitive overall generation fidelity compared to baselines.

Electroencephalography (EEG) generation is essential for alleviating data scarcity and enabling large scale neural modeling in brain computer interface applications. However, existing flow based approaches assume that every channel and every time segment within a sample shares a single global time progression, overlooking the fact that not all EEG moments are equal. To address this overlooked heterogeneity, we propose an adaptive EEG generation framework built on conditional flow matching. The framework introduces Position-Adaptive Time Scheduling, which tracks per position reconstruction error to modulate a position specific time progress within the flow matching trajectory. It further incorporates Factorized Spatio-Temporal Attention and a frequency aligned multi resolution spectral consistency loss to model inter channel dependencies induced by volume conduction and compensate for the power law spectral bias of EEG, thereby improving the quality of generated signals. Extensive experiments on three EEG datasets with distinct acquisition protocols and task semantics show that our framework consistently outperforms the strongest baseline, reducing TS-FID by up to 62.2% and improving downstream classification accuracy gain by up to 6.77 percentage points. These results suggest that the proposed method represents a promising step toward scalable, high fidelity data augmentation for real world brain computer interface applications.

In bearing vibration datasets, most samples receive predicted fault probabilities close to 0 or 1, while samples with intermediate (gray-zone) probabilities are rare. Such borderline samples are important because they reflect conditions in which maintenance decisions may require additional inspection or a conservative response and are useful for studying decision boundaries. To address this scarcity, this paper proposes and compares two approaches that generate vibration signals whose predicted fault probability matches a target probability of 0.25, 0.50, or 0.75. We use the average output of a heterogeneous ensemble classifier with different architectures and random initializations as a fixed, gradient-accessible probability oracle. The first, training-based approach, Probability-Regularized Generative Adversarial Network (PR-GAN), extends Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) and edits a real signal through a residual generator while pushing the classifier output toward the target probability. The second is a training-free, per-sample Wachter-style counterfactual (CF) procedure that directly optimizes each input signal to reach the target probability while remaining close to the source signal. We evaluate both methods on the Case Western Reserve University (CWRU) and Paderborn bearing datasets using mean absolute target-probability error, time-domain total variation, and frequency-domain log power spectral density (log-PSD) differences. Across all settings, CF reaches the target with a mean absolute probability error of 0.005-0.008 and a within-tolerance success rate of 1.000 on retained samples, whereas PR-GAN's mean error is 0.046-0.059 with success rates between 0.501 and 0.680. CF therefore steers the probability more reliably and requires smaller average L1 changes, whereas PR-GAN has a lower reported runtime in most settings.

Many complex systems such as brain networks, financial markets, and gene-regulatory circuits are described not by a fixed graph but by one that changes over time. A standard way to summarise such structure at each instant is the sparse precision (inverse-covariance) matrix, and the time-varying graphical lasso (TVGL) turns a multivariate signal into a smooth chain of these matrices. We introduce TVGL-CFM, a single model that learns the distribution of such chains and can both generate new, realistic time-varying network trajectories for a given class and forecast how an observed trajectory will continue. Each precision matrix lives on a curved space of positive-definite matrices, but a log-Euclidean chart flattens an entire trajectory into an ordinary vector space, so a simple conditional flow-matching model can be trained and sampled there while every decoded matrix is guaranteed to be a valid precision matrix. For forecasting we start the flow not from noise but from a rough extrapolation of the recent history, so the model only has to learn a small correction. Across EEG motor-imagery, chaotic systems, and gene-expression data, TVGL-CFM generates trajectories that keep the class-discriminative structure of real data, and it forecasts future connectivity more accurately than raw-signal baselines. Generating the structured precision trajectory directly is therefore more faithful than generating raw signals and estimating connectivity afterwards.

Mobile usage traces are critical for tasks such as user behavior prediction and app recommendation, yet their use is constrained by privacy restrictions and costly large-scale data collection. Although generative models perform well on general time series, their application to mobile usage data remains challenging because (i) limited user activity causes severe sparsity, (ii) heterogeneous variable types complicate joint modeling, and (iii) functional differences across apps create pronounced usage imbalance. To address these challenges, we propose Multivariate-Imaging Diffusion (MIDiff), a diffusion-based framework operating in an imaging space defined by Cross-Gramian Angular Sum Field (C-GASF). C-GASF transforms sparse multivariate sequences into correlation images, while MIDiff employs Triple Attention in a U-Net to preserve temporal consistency and variable dependencies. Experiments show that MIDiff achieves state-of-the-art performance across fidelity metrics. In particular, it obtains a Discriminative Accuracy (DA) of 0.1526, compared with 0.3476 for the strongest baseline, ZITS-VAE, demonstrating its effectiveness in generating realistic and diverse mobile usage traces. Our code is available at https://github.com/YilaiLiu-HKU/MIDiff.

The accelerating shift toward low-carbon power systems, together with the widespread adoption of behind-the-meter technologies such as rooftop solar and electric vehicles, is placing new operational and analytical demands on electricity grids. At the same time, smart-grid research increasingly relies on machine learning (ML), yet progress is constrained by limited access to high-resolution household energy data due to privacy concerns, regulatory barriers, and collection costs. This work presents WattCouncil, a data-generation framework in which household electricity demand is generated by a council of Large Language Model (LLM)-based agents operating in specialized roles to generate, audit, and validate structured energy scenarios under explicit cultural, temporal, and physical constraints. Rather than acting as static predictors, these agents serve as adaptive decision-makers within a governed pipeline. Motivated by studies highlighting the importance of contextual factors in energy use, our framework produces context-sensitive daily routines through a guided reasoning process that incorporates household composition, temporal factors, and environmental conditions. We evaluate the generated profiles against the detailed CER dataset, which contains over a year of load measurements for 4232 households together with survey-based socio-economic information. We further assess the consistency of the framework through ablation studies. Source code is available at https://github.com/Singularity-AI-Lab/wattcouncil

Generative models have changed how machine learning represents complex data distributions, especially in language and vision, yet many real-world systems are observed instead as continuous, high-dimensional, and noisy sensor time series. Existing generative modeling of sensor data, however, remains fragmented across modalities, datasets, and task formulations, limiting a systematic understanding of when, how, and why generative models succeed or fail in real-world settings. To address this gap, we introduce SensorGen, a large-scale study of sensor-signal generation spanning 14 settings across 4 domains, 7 datasets, and 12 signal modalities. Leveraging SensorGen, we systematically evaluate generative models from five major families and uncover three key findings: (1) flow-matching models provide strong overall performance across most settings; (2) signal properties matter, with demographic covariates improving longitudinal generation and time-frequency modeling improving high-frequency signal generation; and (3) generated signals have practical utility beyond visual realism, with scaling improving generation quality and synthetic data improving downstream performance. Together, SensorGen establishes a broader understanding of design choices, evaluation protocols, and failure modes in real-world sensor data generation.

The generation of synthetic relational databases often involves modeling complex temporal dynamics, such as transaction logs or event sequences. A significant challenge in this domain is the handling of categorical time series (e.g., status codes), where standard encoding methods like one-hot encoding fail to capture intrinsic frequency-domain features such as seasonality and cyclicity. In this paper, we introduce Sequential RC-TGAN (Seq. RC-TGAN), a temporal extension of the RC-TGAN framework, equipped with a novel integrated loss function based on the Spectral Envelope Theory. This differentiable loss allows the generator to directly optimize the preservation of latent periodic structures via backpropagation. While spectral envelope theory is inherently designed for categorical sequences, we extend this frequency-domain regularization to continuous time series by employing a Variational Gaussian Mixture Model (VGM) discretization strategy. To establish a mathematically rigorous evaluation standard, we simulate categorical time series governed by a parameter $α$, with exactly known theoretical spectral envelopes. Integrating these dynamic sequences into the child tables of a relational database yields a robust ground-truth benchmark for evaluating the frequency-domain fidelity of our generative framework. Furthermore, we address the lack of robust evaluation standards for relational time series by proposing two new metrics: Spectral Density Divergence and Spectral Envelope Divergence. Experimental results on real-world datasets, as well as our simulated benchmarks, demonstrate that our end-to-end approach significantly outperforms state-of-the-art systems in reproducing cyclic patterns and long-term seasonality across both categorical and continuous features.

Generative models have achieved remarkable success in data synthesis, though recent advances driven by increasing model scale have introduced challenges in computational cost and efficiency. Quantum machine learning offers a promising alternative, representing complex data distributions using compact, highly expressive models. Here, we propose QDiffusion-TS, the first quantum generative diffusion model for time series synthesis, and validate it on the IQM quantum processor. The framework extends a classical diffusion architecture by replacing feed-forward components within the denoising transformer with quantum neural networks, yielding a hybrid quantum transformer that reduces the number of trainable parameters in each replaced component by nearly three orders of magnitude. Evaluated on financial time series from Apple and Amazon, the model generates synthetic data that more accurately reproduces the real distributions, reducing Wasserstein distance by approximately 44% relative to its classical counterpart across both datasets. In a downstream forecasting task, augmentation with the generated data improves predictive performance by up to 71% in RMSE over a baseline trained solely on real data. These results show that quantum enhanced architectures can consistently match and frequently surpass classical performance with substantially fewer parameters, establishing a practical framework towards more efficient and scalable data-driven generative modelling.

A Prior-data fitted Network learns the posterior predictive induced by its training prior; bringing this paradigm to multivariate time-series classification therefore calls for a synthetic generator that produces complete labelled datasets with temporal structure. We introduce a causal prior that synthesizes each dataset from a randomly sampled DAG over typed nodes across two modalities (tabular attributes and time series), natively producing multivariate, multi-class TSC datasets with cross-modal causal structure across channels, timesteps and labels, a regime not addressed by existing synthetic priors. To validate the prior, we finetune TabPFN v2.5 with minimal adaptations and evaluate on 75 UCR/UEA datasets within TabPFN's operating regime. Finetuning on our generator significantly outperforms both the unmodified upstream model and a tabular-only ablation of the same prior (Wilcoxon signed-rank $p=3.0\times 10^{-8}$ on ROC-AUC), isolating the contribution of the cross-modal temporal structure.

EEG foundation models can learn generalizable representations from large-scale EEG corpora to enable single-backbone transfer across diverse clinical and brain-computer interface tasks. Existing models typically discretize the continuous multi-channel EEG waveform into patches or codebook tokens and train a transformer with masked self-supervision. Recognizing that this discretization fragments continuous brain rhythms and obscures fine-grained temporal dynamics, we present B[FM]$^2$(Brain Foundation Model via Flow Matching), whose inductive bias aligns with the data by pretraining directly on the raw signal using continuous-time flow matching without patches, tokenization, or masking. However, multi-channel EEG signals pose an architectural challenge for flow matching: time is densely sampled and highly autocorrelated (thousands of timepoints), while the electrode axis is short (tens of channels) at distinct scalp positions. To address this time-electrode asymmetry, we introduce SplitUNet, a velocity network that factorizes each block into separate 1D temporal and 1D electrode convolutions and downsamples only along time, preserving electrode topology throughout the hierarchy. B[FM]$^2$ sets a new state of the art on 7 of 9 standard downstream EEG classification tasks, using a pretraining budget of only 36,895 segments ($\approx$ 307h), 1-2 orders of magnitude ($\approx$ 30x) less than required by existing EEG foundation models. Further, it generates synthetic EEGs that two board-certified neurologists cannot distinguish from brain data (Cohen's $κ=$ -0.096). https://jd730.github.io/projects/BFM2

Laboratory tests in electronic health records are collected irregularly, and the absence of a test order can be as informative as the measurement itself. Such missingness reflects clinicians' decisions and patient physiology, making it important to model it directly rather than treat it as a preprocessing artifact. Here we present a diffusion-based approach for generating clinical time series that jointly models laboratory values and their observation patterns using the public Data Analytics Challenge on Missing Data Imputation (DACMI) benchmark derived from MIMIC-III. To preserve realistic sampling, we align chart times into 4-hour intervals and segment admissions into 7-day windows, producing trajectories that pair each lab value with a corresponding observation indicator. Standard transformations and normalization are applied to stabilize training. Our method extends the TimeDiff framework to learn continuous lab values and discrete missingness patterns through complementary diffusion objectives. Experiments show that the generated data closely match real patient trajectories across individual lab distributions and joint value-missingness embeddings, demonstrating that diffusion models can capture clinically meaningful dependencies between patient physiology and clinicians' testing behavior under MNAR-like (missing-not-at-random) missingness. These preliminary results indicate that our model can serve as an initial component toward developing clinical foundation models. By producing synthetic priors that preserve key physiology-missingness relationships, this work motivates the subsequent training of Prior-Data Fitted Networks capable of leveraging informative missingness, which we will investigate in the extended work.

Rare events in time series are critical to model but hard to learn due to data scarcity. Current generative models struggle with extreme values. We observe that rare events leave distinct topological fingerprints - transitions in Betti numbers from point-cloud embeddings - that are more stable and discriminative than statistical moments. We introduce PHINN, a flow-matching framework using dynamic Betti curves as conditioning signals and a persistence landscape loss for homology consistency. It scales to multivariate data, includes a natural-language interface to set Betti targets, supports cross-domain meta-learning and few-shot generation, and provides certified adversarial robustness. On financial, epidemiological, and multi-modal benchmarks, PHINN outperforms statistical and diffusion baselines in topological fidelity (beta-RMSE down 41-63%, transition accuracy up 84%) and matches jump-diffusion models in tail coverage while exceeding them in shape fidelity. All results have 95% confidence intervals.

Synthesizing realistic time series with generative models has wide-ranging applications in real-world scenarios. Despite recent progress, most existing methods are trained under the assumption of abundant training data, which substantially limits their effectiveness in data-scarce settings. In this paper, we propose TimeMoDE, a novel framework that integrates Diffusion Transformers with Mixture-of-Experts to exploit both domain adaptability and diffusion-stage awareness for time series generation under data scarcity. It is pre-trained on a large-scale collection of multi-domain datasets to extract domain-agnostic temporal representations and domain-specific information benefiting generalization during fine-tuning. We propose Domain Prompts to condition expert assignment for indistinguishable noised tokens, mitigating the limitations of capturing inter-dataset relationships. Moreover, we incorporate diffusion timestep signals to equip the experts with awareness of time series degradation variations, facilitating adaptive calibrate to stage-dependent denoising requirements. Extensive experiments demonstrate that TimeMoDE outperforms existing methods under diverse low-data settings. It establishes an innovative paradigm for advanced time series few-shot generation.

Flow matching and diffusion models enable conditional generation across domains ranging from images to proteins, with recent extensions to out-of-distribution contexts. Yet generative models of neural time series have largely remained restricted to categorical conditioning, precluding compositional and zero-shot generalization. In this work, we propose a per-timestep conditioned diffusion transformer for generating realistic fMRI brain dynamics during unseen cognitive tasks by injecting both compositional language and optional spatial priors in-context. Such zero-shot generation could enable counterfactual neuroscience by supporting in-silico design and evaluation of novel cognitive experiments before empirical validation. Leveraging this model, we evaluate across hundreds of held-out task conditions and characterize predictive performance in relation to the training manifold. From language alone, the model recovers region-specific recruitment across tasks and held-out spatial activation patterns. Spatial priors, when available, complement the text pathway by anchoring generation in regions of task space where language alone degrades, while retaining the compositional structure needed for counterfactual task specification. To our knowledge this is the first generative model of whole-cortex fMRI dynamics for unseen cognitive tasks, advancing counterfactual neuroscience and data-driven experimental design.

In time-series generation, existing approaches typically handcraft ortrain a separate model for each dataset, which hinders their scalability and fails to leverage shared temporal structures across domains. To address this fragmentation, we propose UPLOTS, a Unified, Prompt-guided Language model framework fOr constrained Time-Series Generation across diverse domains. Instead of building task-specific models, UPLOTS leverages a single pre-trained transformer backbone guided by learned constraint prompts, enabling on-demand generation with precise pattern control. One key innovation is our dynamic multi-dataset loss re-weighting and prompt-to-pattern mapping, which allows UPLOTS to internalize diverse temporal structures during training and conditionally generate them at inference. We evaluate UPLOTS on four real-world benchmarks and multiple constraint settings, including peak-period, calendar, load-level, and volatility patterns. Additional held-out constraint-combination and downstream forecasting experiments further demonstrate that UPLOTS generalizes beyond the original peak-pattern setting and improves data augmentation under scarce real-data regimes. Our code and baselines are available at github repo: https://github.com/cruiseresearchgroup/UPLOTS.

Surface winds can vary substantially from one minute to the next, so there is scope for studying its variation on this fine time scale. Restricting to the month of June to minimize seasonality, this work develops a range of machine learning models for generating realistic time series of surface wind vectors at a site in Lamont, Oklahoma based on more than 30 years of high quality measurements at the minute time scale. Such a generator could be used as an input into models from a range of disciplines, notably for wind energy, but also wildfire spread and aviation, among others. The data show complex diurnal structures in both wind speed and direction that would be challenging to capture with standard time series models, so we consider a number of machine learning approaches to producing a stochastic wind generator based on time vector-quantized variational autoencoders. We consider generating a day's worth of data at a time and generating a day of wind vectors conditional on the previous day's winds. We also study methods for incorporating a discrete weather state variable in the generator. We evaluate the generators using a wide range of formal and informal methods. The best of these generators can capture many but not all of the complex features present in the observational data. In particular, the best of our approaches accurately mimic diurnal changes in wind volatility but struggle to match the observed distribution of extreme wind speeds.

Generating realistic synthetic sequential data is critical in real-world applications across operations research, finance, healthcare, energy systems, and scientific computing, where time-indexed observations are used for prediction, simulation, risk assessment, and data-driven decision-making. While diffusion models have achieved remarkable success in generating static data, their direct extensions to sequential settings often fail to capture temporal dependence and information structure. Designing diffusion models that can simulate sequential data in an adapted manner, and hence without anticipation of future information, therefore remains an open challenge. In this work, we propose a sequential forward-backward diffusion framework for adapted time series generation. Our approach progressively injects and removes noise along the sequence, conditioning on the previously generated history to ensure adaptiveness. A novel score-matching objective is introduced for efficient parallel training. We derive rigorous statistical guarantees under a generic framework, then establish score approximation, score estimation, and distribution estimation results with ReLU networks serving as a concrete instance. Empirically, we validate our method on synthetic data, including ARMA models and Gaussian processes, and demonstrate its effectiveness in constructing mean-variance optimal portfolios.

Generating realistic financial time series is challenging as training data is often limited to a single historical path. With such scarce data, overfitting is hard to avoid, especially under adversarial training where a trained discriminator can memorize the training samples. To mitigate this, recent approaches train generators to minimize the discrepancy between untrained feature representations of real and generated time series. In these works, the feature maps are based on path signatures, which can fail to capture relevant time series properties at tractable truncation depths. In this work, we instead train generators by matching random convolutional features of real and generated time series. Existing random convolutional feature maps, such as Rocket and Hydra, have been shown to provide informative representations of real-world time series, but cannot supervise generative models because they are non-differentiable. We introduce SOCK (SOft Competing Kernels), a fully differentiable random convolutional feature map, suited to train generative time series models. We show that generators trained by matching random SOCK features consistently outperform signature and diffusion baselines across a wide range of small-sample financial datasets. We further demonstrate SOCK's expressiveness on two-sample hypothesis testing and time series classification tasks, where SOCK matches or outperforms existing unsupervised feature maps.

Training robust multivariate time series forecasting models requires large, diverse corpora, yet many real-world domains provide only a handful of observed sequences. Existing generators fail to resolve this mismatch: prior-based approaches (e.g., CauKer, TimePFN) produce domain-agnostic samples, while data-driven methods (e.g., TimeGAN) treat references as black-box supervision, forfeiting explicit control over periodic structure, local variability, and cross-variable dynamics. We propose ReGeN, a reference-guided generative pipeline that treats observed sequences not as examples to imitate, but as structural scaffolds for controllable synthesis. ReGeN decomposes each reference into three interpretable components: a phase-aligned periodic backbone capturing dominant domain morphology; per-variable stochastic residuals modeled with a deep-kernel Gaussian process; and lag-aware cross-variable dependencies injected through a structural causal model with fitted coupling coefficients. Sampling these components at controllable temperature broadens distributional coverage while preserving domain-grounded structure. We show that ReGeN-generated data consistently substitutes for real sibling data with minimal forecasting degradation, and in strongly periodic domains such as traffic, can outperform the real source itself. We further show that a foundation model pretrained on ReGeN corpora outperforms those pretrained on prior-based and data-driven synthetic alternatives. This suggests that in low-data regimes, how reference data is structurally exploited can matter as much as how much data is available.

Generating realistic time series is essential for scientific research and real-world applications. However, existing methods often emphasize overall distributional fidelity while failing to faithfully capture extreme events. To advance existing research, we propose E4GEN, an explainable diffusion framework for extreme event-aware time-series generation. E4GEN provides systematic insights into when, what, and how to control extreme-event generation through three key components. First, E-Activator learns the dataset-adaptive extreme-control signal activation step during the denoising process without interfering with regular temporal components, including trend and seasonality. Second, E-Predictor determines what control signal to enforce through Self-Driven Semantic Prediction, where each sample derives its own control signal by inferring latent extreme-event information during generation. It also includes a novel Data-Conditioned Training, Noise-Initiated Sampling mechanism to address the issue of unavailable training labels. Third, E-Control specifies how to control extreme-event generation through a trainable Extreme Control Network, which transforms the semantic control signal into layer-wise signals and injects it into the denoising process. We evaluate E4GEN on six datasets with 17 metrics, and extensive experiments show that E4GEN outperforms state-of-the-art models across multiple dimensions, including overall fidelity, extreme-event fidelity, and downstream utility.

While Next-Token Prediction (NTP) has unified LLM pretraining, its adaptation to unbounded, continuous time series (TS) remains open. To bridge the gap, we introduce UniTok, a universal tokenizer that transforms TS into discrete tokens, and UniTok-FM, a foundation model pretrained via NTP on these tokens. UniTok-FM is a general-purpose foundation model that supports zero-shot and prompt-boosted forecasting, as well as few-shot generation and classification via training-free in-context inference--a capability not achieved by prior works. Technically, UniTok is a vector-quantized autoencoder incorporating prefix normalization for scale stabilization, a progressive-resolution causal architecture for encoding and decoding, and a structure-preserving reconstruction loss for training. UniTok-FM adopts an off-the-shelf LLM architecture without TS-specific modifications. Instead of pretraining on isolated TS, it performs NTP on context windows formed by multiple series with similar patterns, aiming to capture their shared dynamics. Experiments on forecasting, generation, and classification show that a single unified UniTok-FM consistently outperforms statistical and supervised baselines, achieves competitive performance with task-specific foundation models, and uniquely enables training-free in-context inference across tasks.

Functional Magnetic Resonance Imaging (fMRI) provides non-invasive access to dynamic brain activity by measuring blood oxygen level-dependent (BOLD) signals over time. However, the resource-intensive nature of fMRI acquisition limits the availability of high-fidelity samples required for data-driven brain analysis models. While modern generative models can synthesize fMRI data, they often remain challenging in replicating their inherent non-stationarity, intricate spatiotemporal dynamics, and physiological variations of raw BOLD signals. To address these challenges, we propose Dual-Spectral Flow Matching (DSFM), a novel fMRI generative framework that cascades dual frequency representation of BOLD signals with spectral flow matching. Specifically, our framework first converts BOLD signals into a wavelet decomposition map via a discrete wavelet transform (DWT) to capture globalized transient and multi-scale variations, and projects into the discrete cosine transform (DCT) space across brain regions and time to exploit localized energy compaction of low-frequency dominant BOLD coefficients. Subsequently, a spectral flow matching model is trained to generate class-conditioned cosine-frequency representation. The generated samples are reconstructed through inverse DCT and inverse DWT operations to recover physiologically plausible time-domain BOLD signals. This dual-transform approach imposes structured frequency priors and preserves key physiological brain dynamics. Ultimately, we demonstrate the efficacy of our approach through improved downstream fMRI-based brain network classification. The code is available at https://github.com/htew0001/DSFM.git .

Recent work on the sequence universality of State Space Models (SSMs) has introduced efficient, maximally expressive continuous-time approaches for time-series modelling. While these works focus on discriminative settings, we extend this perspective to generative time-series modelling by proving that maximally expressive Structured Linear Controlled Differential Equations (SLiCEs) are universal time-series generators, in the sense that they can approximate the induced path laws of continuous causal pushforwards on compact latent sets in $W_\infty$. Building on these theoretical results, we propose Generative SLiCEs (G-SLiCEs), a maximally expressive continuous-time model for flow matching on path-space. Empirically, we show that expressivity improves performance in probabilistic forecasting and downstream tasks, while retaining the advantages of continuous-time models such as generalising to arbitrary observation grids. This is particularly beneficial for irregular grids, where fixed-grid models often struggle.

In recent years, financial institutions and firms have increasingly adopted synthetic data to address data scarcity and to generate counterfactual market scenarios. However, reproducing all the statistical properties of financial time series, commonly known as stylized facts, remains an open challenge for many existing general-purpose architectures. In this paper, we present a quality-aware generative framework that combines two classes of generative methods, demonstrating how their integration addresses existing limitations while enhancing the realism of synthetic data. Specifically, we first introduce CoMeTS-GAN (Correlated Multivariate Time Series GAN), a Conditional Generative Adversarial Network (C-GAN) designed to jointly generate mid-price and volume time-series for correlated stocks. We then show how our GAN architecture can be incorporated into state-of-the-art diffusion models to enhance the quality of generated correlation structures. Specifically, the GAN's Critic serves as a quality evaluation module that guides the diffusion process, enforcing learned correlation structures in the generated time-series. Our framework offers a lightweight and responsive solution for realistic stock market simulation, explicitly modeling inter-asset correlation structures. We experimentally validate our framework against leading generative architectures, showing that it more effectively captures the stylized facts of stock markets and models inter-asset correlations.

Schrödinger bridges for time series (SBTS) generate synthetic paths by projecting, in relative entropy, a Brownian reference onto the path laws that match the joint distribution of the data on the observation grid. The Brownian reference, however, fixes the quadratic variation of the generated paths, which is restrictive when stochastic volatility, correlated noise, or rank-deficient covariance structures must be reproduced. We introduce "Triangular-Reference Schrödinger Bridges for Time Series" (TR-SBTS), which keeps the entropy-projection backbone of SBTS but replaces the Brownian reference by a triangular, volatility-informed, intervalwise frozen reference on a state augmented with latent covariance descriptors. The construction remains a single entropy projection on the augmented state: the minimiser is the $h$-transform of the reference, and on each frozen interval the optimal drift has the logarithmic-gradient form $b^\star(t,x)=A\,\nabla\log H(t,x)$, intrinsic to the active covariance directions when the frozen covariance $A$ is degenerate. We prove stability of the frozen approximation and consistency of the associated regularised kernel estimators, describe a reference-aware Nadaraya--Watson implementation of the conditional next-increment law, and evaluate the construction on numerical experiments.

Accurate carbon emission monitoring is critical for climate policy and emerging regulatory mechanisms such as the EU Carbon Border Adjustment Mechanism, yet city-level high-frequency monitoring data remain extremely scarce, severely limiting data-hungry deep learning models. Time series generation is a natural remedy, but existing GAN and diffusion-based generators often provide limited explicit supervision for the domain structure of carbon emission data: they may match marginal distributional statistics while insufficiently preserving cross-variable correlations between CO$_2$ and co-emitted pollutants and meteorological factors, and tend to collapse the first-difference statistics of atmospheric measurements, producing sequences that are smooth on average but lack the realistic step-wise variability of the underlying signals. We propose TriHead-GAN, a Transformer-based adversarial framework whose triple-head discriminator jointly supervises three complementary aspects of the joint distribution: distributional authenticity via a Wasserstein critic, cross-variable dependency via leakage-free regression of the target variable, and step-wise temporal smoothness via adjacent-difference prediction. The generator combines global self-attention with local temporal convolution, per-step noise injection, and an anti-smoothing loss that matches first-difference statistics. Experiments on the self-collected Changsha Carbon dataset, two public carbon datasets (China, US), and the ETTh1 benchmark show that TriHead-GAN achieves favorable performance over mainstream baselines on the vast majority of settings, and that the resulting synthetic windows improve downstream forecasting accuracy in low-resource carbon monitoring scenarios.

Generating high-quality time-series data is challenging because real-world signals often exhibit multimodal patterns and multiscale dynamics, including oscillations and high-frequency variations. Flow Matching (FM) offers an efficient alternative to diffusion models, but practical implementations typically rely on a single finite-capacity global vector-field estimator. In such heterogeneous temporal distributions, distinct regimes may pass through nearby flow states while requiring incompatible conditional velocities. A monolithic estimator trained with the standard $\ell_2$ velocity-matching objective may therefore learn an overly smoothed approximation of the local transport field. This estimator-level smoothing can attenuate branch-specific dynamics, leading to spectral distortion and poor mode coverage. To address this, we propose PrismFlow, a new FM method with Koopman-inspired dynamical experts. Each expert learns residual corrections in a latent space where local nonlinear temporal evolution can be approximated by linear transitions. We further propose a confidence-aware Winner-Take-All (WTA) objective that updates only the expert best aligned with each sample while masking gradients to the others, encouraging mode-specific specialization. During sampling, the selected expert adds a residual dynamical correction to the global transport field, preserving FM stability while recovering fine-grained and high-frequency temporal structures. Across various benchmarks, PrismFlow effectively mitigates the spectral contraction in standard FM and achieves state-of-the-art performance, with a 15.6% gain in Context-FID and a 38.6% improvement in Discriminative Score, while remaining robust in low-data settings and effective for forecasting and imputation.

Diagnosing Major Depressive Disorder (MDD) from functional magnetic resonance imaging (fMRI) using functional connectivity (FC) analysis requires large amounts of labeled data that are scarce in clinical settings. Existing augmentation methods synthesize FC matrices, which compress fMRI recordings into static pairwise summaries and discard temporal information. We propose fMRI-Diffusion, a framework that synthesizes region-of-interest (ROI)-level fMRI time series rather than FC matrices. A Temporal Transformer serves as the denoising network within a denoising diffusion probabilistic model, treating each time point as a token to capture temporal dependencies through self-attention. A supervised pretraining strategy initializes the Transformer with task-relevant representations before diffusion training, and FC matrices are derived from the synthesized time series for classification. Experiments on the REST-meta-MDD dataset show that augmenting training data with synthetic time series consistently improves diagnostic accuracy across ten classifiers, six parcellation atlases, and three acquisition sites. The method outperforms five recent FC-based synthesis approaches, with accuracy gains of up to 3.7 percentage points over the strongest baseline. Ablation studies confirm the contributions of both the Transformer-based denoiser and the pretraining strategy. Distributional fidelity metrics remain below 0.06 across all conditions, indicating close agreement between real and synthetic distributions. These findings suggest that synthesizing fMRI time series before FC computation preserves temporal information lost in matrix-level augmentation and provides a practical strategy for MDD diagnosis under limited data.

High-fidelity EEG generation is critical for alleviating data scarcity and addressing privacy constraints in large-scale neural modeling. Despite recent progress, most existing approaches formulate EEG generation via discrete denoising objectives, which inadequately reflect the inherently continuous temporal dynamics and spectral structure of neural activity. As a result, these methods often struggle to preserve long-range temporal dependencies and exhibit mismatches in the spectral and temporal structure of the generated signals. In this work, we argue that effective EEG generation requires models that operate directly on the continuous evolution of neural signals. We introduce Just EEG Transformer (JET), a generative framework based on conditional flow matching that models EEG as raw sequences evolving along continuous trajectories. By learning a smooth vector field that transports noise to the EEG data distribution, JET captures temporal continuity and transient dynamics without relying on discretized denoising schemes or domain-specific representations. To ensure that the learned dynamics remain consistent with key properties of EEG signals, we introduce principled constraints that preserve spectral structure, temporal stationarity, and signal-level statistics. Across three large-scale benchmarks, JET consistently achieves state-of-the-art performance, reducing TS-FID by over 40% compared to strong baselines. Extensive analyses show that JET captures key structural properties of neural dynamics, providing a scalable and principled approach to EEG generation. Project page: https://y-research-sbu.github.io/JET/ .