Text-to-Time Series generation holds significant potential to address challenges such as data sparsity, imbalance, and limited availability of multimodal time series datasets across domains. While diffusion models have achieved remarkable success in Text-to-X (e.g., vision and audio data) generation, their use in time series generation remains in its nascent stages. Existing approaches face two critical limitations: (1) the lack of systematic exploration of general-proposed time series captions, which are often domain-specific and struggle with generalization; and (2) the inability to generate time series of arbitrary lengths, limiting their applicability to real-world scenarios. In this work, we first categorize time series captions into three levels: point-level, fragment-level, and instance-level. Additionally, we introduce a new fragment-level dataset containing over 600,000 high-resolution time series-text pairs. Second, we propose Text-to-Series (T2S), a diffusion-based framework that bridges the gap between natural language and time series in a domain-agnostic manner. T2S employs a length-adaptive variational autoencoder to encode time series of varying lengths into consistent latent embeddings. On top of that, T2S effectively aligns textual representations with latent embeddings by utilizing Flow Matching and employing Diffusion Transformer as the denoiser. We train T2S in an interleaved paradigm across multiple lengths, allowing it to generate sequences of any desired length. Extensive evaluations demonstrate that T2S achieves state-of-the-art performance across 13 datasets spanning 12 domains.
Tabular data generation has recently attracted a growing interest due to its different application scenarios. However, generating time series of tabular data, where each element of the series depends on the others, remains a largely unexplored domain. This gap is probably due to the difficulty of jointly solving different problems, the main of which are the heterogeneity of tabular data (a problem common to non-time-dependent approaches) and the variable length of a time series. In this paper, we propose a Diffusion Transformers (DiTs) based approach for tabular data series generation. Inspired by the recent success of DiTs in image and video generation, we extend this framework to deal with heterogeneous data and variable-length sequences. Using extensive experiments on six datasets, we show that the proposed approach outperforms previous work by a large margin.
Generating temporal data under constraints is critical for forecasting, imputation, and synthesis. These datasets often include auxiliary conditions that influence the values within the time series signal. Existing methods face three key challenges: (1) they fail to adapt to conditions at inference time; (2) they rely on sequential generation, which slows the generation speed; and (3) they inefficiently encode categorical features, leading to increased sparsity and input sizes. We propose WaveStitch, a novel method that addresses these challenges by leveraging denoising diffusion probabilistic models to efficiently generate accurate temporal data under given auxiliary constraints. WaveStitch overcomes these limitations by: (1) modeling interactions between constraints and signals to generalize to new, unseen conditions; (2) enabling the parallel synthesis of sequential segments with a novel "stitching" mechanism to enforce coherence across segments; and (3) encoding categorical features as compact periodic signals while preserving temporal patterns. Extensive evaluations across diverse datasets highlight WaveStitch's ability to generalize to unseen conditions during inference, achieving up to a 10x lower mean-squared-error compared to the state-of-the-art methods. Moreover, WaveStitch generates data up to 460x faster than autoregressive methods while maintaining comparable accuracy. By efficiently encoding categorical features, WaveStitch provides a robust and efficient solution for temporal data generation. Our code is open-sourced: https://github.com/adis98/HierarchicalTS
In this paper, we introduce Neural Mapper for Vector Quantized Time Series Generator (NM-VQTSG), a novel method aimed at addressing fidelity challenges in vector quantized (VQ) time series generation. VQ-based methods, such as TimeVQVAE, have demonstrated success in generating time series but are hindered by two critical bottlenecks: information loss during compression into discrete latent spaces and deviations in the learned prior distribution from the ground truth distribution. These challenges result in synthetic time series with compromised fidelity and distributional accuracy. To overcome these limitations, NM-VQTSG leverages a U-Net-based neural mapping model to bridge the distributional gap between synthetic and ground truth time series. To be more specific, the model refines synthetic data by addressing artifacts introduced during generation, effectively aligning the distributions of synthetic and real data. Importantly, NM-VQTSG can be used for synthetic time series generated by any VQ-based generative method. We evaluate NM-VQTSG across diverse datasets from the UCR Time Series Classification archive, demonstrating its capability to consistently enhance fidelity in both unconditional and conditional generation tasks. The improvements are evidenced by significant improvements in FID, IS, and conditional FID, additionally backed up by visual inspection in a data space and a latent space. Our findings establish NM-VQTSG as a new method to improve the quality of synthetic time series. Our implementation is available on \url{https://github.com/ML4ITS/TimeVQVAE}.
Data augmentation can significantly enhance the performance of machine learning tasks by addressing data scarcity and improving generalization. However, generating time series data presents unique challenges. A model must not only learn a probability distribution that reflects the real data distribution but also capture the conditional distribution at each time step to preserve the inherent temporal dependencies. To address these challenges, we introduce AVATAR, a framework that combines Adversarial Autoencoders (AAE) with Autoregressive Learning to achieve both objectives. Specifically, our technique integrates the autoencoder with a supervisor and introduces a novel supervised loss to assist the decoder in learning the temporal dynamics of time series data. Additionally, we propose another innovative loss function, termed distribution loss, to guide the encoder in more efficiently aligning the aggregated posterior of the autoencoder's latent representation with a prior Gaussian distribution. Furthermore, our framework employs a joint training mechanism to simultaneously train all networks using a combined loss, thereby fulfilling the dual objectives of time series generation. We evaluate our technique across a variety of time series datasets with diverse characteristics. Our experiments demonstrate significant improvements in both the quality and practical utility of the generated data, as assessed by various qualitative and quantitative metrics.
Diffusion models have shown promising ability in generating high-quality time series (TS) data. Despite the initial success, existing works mostly focus on the authenticity of data at the individual level, but pay less attention to preserving the population-level properties on the entire dataset. Such population-level properties include value distributions for each dimension and distributions of certain functional dependencies (e.g., cross-correlation, CC) between different dimensions. For instance, when generating house energy consumption TS data, the value distributions of the outside temperature and the kitchen temperature should be preserved, as well as the distribution of CC between them. Preserving such TS population-level properties is critical in maintaining the statistical insights of the datasets, mitigating model bias, and augmenting downstream tasks like TS prediction. Yet, it is often overlooked by existing models. Hence, data generated by existing models often bear distribution shifts from the original data. We propose Population-aware Diffusion for Time Series (PaD-TS), a new TS generation model that better preserves the population-level properties. The key novelties of PaD-TS include 1) a new training method explicitly incorporating TS population-level property preservation, and 2) a new dual-channel encoder model architecture that better captures the TS data structure. Empirical results in major benchmark datasets show that PaD-TS can improve the average CC distribution shift score between real and synthetic data by 5.9x while maintaining a performance comparable to state-of-the-art models on individual-level authenticity.
Benchmarking anomaly detection approaches for multivariate time series is a challenging task due to a lack of high-quality datasets. Current publicly available datasets are too small, not diverse and feature trivial anomalies, which hinders measurable progress in this research area. We propose a solution: a diverse, extensive, and non-trivial dataset generated via state-of-the-art simulation tools that reflects realistic behaviour of an automotive powertrain, including its multivariate, dynamic and variable-state properties. Additionally, our dataset represents a discrete-sequence problem, which remains unaddressed by previously-proposed solutions in literature. To cater for both unsupervised and semi-supervised anomaly detection settings, as well as time series generation and forecasting, we make different versions of the dataset available, where training and test subsets are offered in contaminated and clean versions, depending on the task. We also provide baseline results from a selection of approaches based on deterministic and variational autoencoders, as well as a non-parametric approach. As expected, the baseline experimentation shows that the approaches trained on the semi-supervised version of the dataset outperform their unsupervised counterparts, highlighting a need for approaches more robust to contaminated training data. Furthermore, results show that the threshold used can have a large influence on detection performance, hence more work needs to be invested in methods to find a suitable threshold without the need for labelled data.
Time series generation has emerged as an essential tool for analyzing temporal data across numerous fields. While diffusion models have recently gained significant attention in generating high-quality time series, they tend to be computationally demanding and reliant on complex stochastic processes. To address these limitations, we introduce FM-TS, a rectified Flow Matching-based framework for Time Series generation, which simplifies the time series generation process by directly optimizing continuous trajectories. This approach avoids the need for iterative sampling or complex noise schedules typically required in diffusion-based models. FM-TS is more efficient in terms of training and inference. Moreover, FM-TS is highly adaptive, supporting both conditional and unconditional time series generation. Notably, through our novel inference design, the model trained in an unconditional setting can seamlessly generalize to conditional tasks without the need for retraining. Extensive benchmarking across both settings demonstrates that FM-TS consistently delivers superior performance compared to existing approaches while being more efficient in terms of training and inference. For instance, in terms of discriminative score, FM-TS achieves 0.005, 0.019, 0.011, 0.005, 0.053, and 0.106 on the Sines, Stocks, ETTh, MuJoCo, Energy, and fMRI unconditional time series datasets, respectively, significantly outperforming the second-best method which achieves 0.006, 0.067, 0.061, 0.008, 0.122, and 0.167 on the same datasets. We have achieved superior performance in solar forecasting and MuJoCo imputation tasks, significantly enhanced by our innovative $t$ power sampling method. The code is available at https://github.com/UNITES-Lab/FMTS.
Current Generative Adversarial Network (GAN)-based approaches for time series generation face challenges such as suboptimal convergence, information loss in embedding spaces, and instability. To overcome these challenges, we introduce an advanced framework that integrates the advantages of an autoencoder-generated embedding space with the adversarial training dynamics of GANs. This method employs two discriminators: one to specifically guide the generator and another to refine both the autoencoder's and generator's output. Additionally, our framework incorporates a novel autoencoder-based loss function and supervision from a teacher-forcing supervisor network, which captures the stepwise conditional distributions of the data. The generator operates within the latent space, while the two discriminators work on latent and feature spaces separately, providing crucial feedback to both the generator and the autoencoder. By leveraging this dual-discriminator approach, we minimize information loss in the embedding space. Through joint training, our framework excels at generating high-fidelity time series data, consistently outperforming existing state-of-the-art benchmarks both qualitatively and quantitatively across a range of real and synthetic multivariate time series datasets.
Generating time series data using Generative Adversarial Networks (GANs) presents several prevalent challenges, such as slow convergence, information loss in embedding spaces, instability, and performance variability depending on the series length. To tackle these obstacles, we introduce a robust framework aimed at addressing and mitigating these issues effectively. This advanced framework integrates the benefits of an Autoencoder-generated embedding space with the adversarial training dynamics of GANs. This framework benefits from a time series-based loss function and oversight from a supervisory network, both of which capture the stepwise conditional distributions of the data effectively. The generator functions within the latent space, while the discriminator offers essential feedback based on the feature space. Moreover, we introduce an early generation algorithm and an improved neural network architecture to enhance stability and ensure effective generalization across both short and long time series. Through joint training, our framework consistently outperforms existing benchmarks, generating high-quality time series data across a range of real and synthetic datasets with diverse characteristics.
Score-based diffusion models have recently emerged as state-of-the-art generative models for a variety of data modalities. Nonetheless, it remains unclear how to adapt these models to generate long multivariate time series. Viewing a time series as the discretization of an underlying continuous process, we introduce SigDiffusion, a novel diffusion model operating on log-signature embeddings of the data. The forward and backward processes gradually perturb and denoise log-signatures preserving their algebraic structure. To recover a signal from its log-signature, we provide new closed-form inversion formulae expressing the coefficients obtained by expanding the signal in a given basis (e.g. Fourier or orthogonal polynomials) as explicit polynomial functions of the log-signature. Finally, we show that combining SigDiffusion with these inversion formulae results in highly realistic time series generation, competitive with the current state-of-the-art on various datasets of synthetic and real-world examples.
Generating high-fidelity time series data using generative adversarial networks (GANs) remains a challenging task, as it is difficult to capture the temporal dependence of joint probability distributions induced by time-series data. Towards this goal, a key step is the development of an effective discriminator to distinguish between time series distributions. We propose the so-called PCF-GAN, a novel GAN that incorporates the path characteristic function (PCF) as the principled representation of time series distribution into the discriminator to enhance its generative performance. On the one hand, we establish theoretical foundations of the PCF distance by proving its characteristicity, boundedness, differentiability with respect to generator parameters, and weak continuity, which ensure the stability and feasibility of training the PCF-GAN. On the other hand, we design efficient initialisation and optimisation schemes for PCFs to strengthen the discriminative power and accelerate training efficiency. To further boost the capabilities of complex time series generation, we integrate the auto-encoder structure via sequential embedding into the PCF-GAN, which provides additional reconstruction functionality. Extensive numerical experiments on various datasets demonstrate the consistently superior performance of PCF-GAN over state-of-the-art baselines, in both generation and reconstruction quality. Code is available at https://github.com/DeepIntoStreams/PCF-GAN.
Denoising diffusion probabilistic models (DDPMs) are becoming the leading paradigm for generative models. It has recently shown breakthroughs in audio synthesis, time series imputation and forecasting. In this paper, we propose Diffusion-TS, a novel diffusion-based framework that generates multivariate time series samples of high quality by using an encoder-decoder transformer with disentangled temporal representations, in which the decomposition technique guides Diffusion-TS to capture the semantic meaning of time series while transformers mine detailed sequential information from the noisy model input. Different from existing diffusion-based approaches, we train the model to directly reconstruct the sample instead of the noise in each diffusion step, combining a Fourier-based loss term. Diffusion-TS is expected to generate time series satisfying both interpretablity and realness. In addition, it is shown that the proposed Diffusion-TS can be easily extended to conditional generation tasks, such as forecasting and imputation, without any model changes. This also motivates us to further explore the performance of Diffusion-TS under irregular settings. Finally, through qualitative and quantitative experiments, results show that Diffusion-TS achieves the state-of-the-art results on various realistic analyses of time series.
Generating time series data is a promising approach to address data deficiency problems. However, it is also challenging due to the complex temporal properties of time series data, including local correlations as well as global dependencies. Most existing generative models have failed to effectively learn both the local and global properties of time series data. To address this open problem, we propose a novel time series generative model named 'Time-Transformer AAE', which consists of an adversarial autoencoder (AAE) and a newly designed architecture named 'Time-Transformer' within the decoder. The Time-Transformer first simultaneously learns local and global features in a layer-wise parallel design, combining the abilities of Temporal Convolutional Networks and Transformer in extracting local features and global dependencies respectively. Second, a bidirectional cross attention is proposed to provide complementary guidance across the two branches and achieve proper fusion between local and global features. Experimental results demonstrate that our model can outperform existing state-of-the-art models in 5 out of 6 datasets, specifically on those with data containing both global and local properties. Furthermore, we highlight our model's advantage on handling this kind of data via an artificial dataset. Finally, we show our model's ability to address a real-world problem: data augmentation to support learning with small datasets and imbalanced datasets.
Neural SDEs are continuous-time generative models for sequential data. State-of-the-art performance for irregular time series generation has been previously obtained by training these models adversarially as GANs. However, as typical for GAN architectures, training is notoriously unstable, often suffers from mode collapse, and requires specialised techniques such as weight clipping and gradient penalty to mitigate these issues. In this paper, we introduce a novel class of scoring rules on pathspace based on signature kernels and use them as objective for training Neural SDEs non-adversarially. By showing strict properness of such kernel scores and consistency of the corresponding estimators, we provide existence and uniqueness guarantees for the minimiser. With this formulation, evaluating the generator-discriminator pair amounts to solving a system of linear path-dependent PDEs which allows for memory-efficient adjoint-based backpropagation. Moreover, because the proposed kernel scores are well-defined for paths with values in infinite dimensional spaces of functions, our framework can be easily extended to generate spatiotemporal data. Our procedure permits conditioning on a rich variety of market conditions and significantly outperforms alternative ways of training Neural SDEs on a variety of tasks including the simulation of rough volatility models, the conditional probabilistic forecasts of real-world forex pairs where the conditioning variable is an observed past trajectory, and the mesh-free generation of limit order book dynamics.
We present a novel time series anomaly detection method that achieves excellent detection accuracy while offering a superior level of explainability. Our proposed method, TimeVQVAE-AD, leverages masked generative modeling adapted from the cutting-edge time series generation method known as TimeVQVAE. The prior model is trained on the discrete latent space of a time-frequency domain. Notably, the dimensional semantics of the time-frequency domain are preserved in the latent space, enabling us to compute anomaly scores across different frequency bands, which provides a better insight into the detected anomalies. Additionally, the generative nature of the prior model allows for sampling likely normal states for detected anomalies, enhancing the explainability of the detected anomalies through counterfactuals. Our experimental evaluation on the UCR Time Series Anomaly archive demonstrates that TimeVQVAE-AD significantly surpasses the existing methods in terms of detection accuracy and explainability. We provide our implementation on GitHub: https://github.com/ML4ITS/TimeVQVAE-AnomalyDetection.
Generating realistic time series data is important for many engineering and scientific applications. Existing work tackles this problem using generative adversarial networks (GANs). However, GANs are unstable during training, and they can suffer from mode collapse. While variational autoencoders (VAEs) are known to be more robust to the these issues, they are (surprisingly) less considered for time series generation. In this work, we introduce Koopman VAE (KoVAE), a new generative framework that is based on a novel design for the model prior, and that can be optimized for either regular and irregular training data. Inspired by Koopman theory, we represent the latent conditional prior dynamics using a linear map. Our approach enhances generative modeling with two desired features: (i) incorporating domain knowledge can be achieved by leveraging spectral tools that prescribe constraints on the eigenvalues of the linear map; and (ii) studying the qualitative behavior and stability of the system can be performed using tools from dynamical systems theory. Our results show that KoVAE outperforms state-of-the-art GAN and VAE methods across several challenging synthetic and real-world time series generation benchmarks. Whether trained on regular or irregular data, KoVAE generates time series that improve both discriminative and predictive metrics. We also present visual evidence suggesting that KoVAE learns probability density functions that better approximate the empirical ground truth distribution.
Synthetic Time Series Generation (TSG) is crucial in a range of applications, including data augmentation, anomaly detection, and privacy preservation. Although significant strides have been made in this field, existing methods exhibit three key limitations: (1) They often benchmark against similar model types, constraining a holistic view of performance capabilities. (2) The use of specialized synthetic and private datasets introduces biases and hampers generalizability. (3) Ambiguous evaluation measures, often tied to custom networks or downstream tasks, hinder consistent and fair comparison. To overcome these limitations, we introduce \textsf{TSGBench}, the inaugural Time Series Generation Benchmark, designed for a unified and comprehensive assessment of TSG methods. It comprises three modules: (1) a curated collection of publicly available, real-world datasets tailored for TSG, together with a standardized preprocessing pipeline; (2) a comprehensive evaluation measures suite including vanilla measures, new distance-based assessments, and visualization tools; (3) a pioneering generalization test rooted in Domain Adaptation (DA), compatible with all methods. We have conducted comprehensive experiments using \textsf{TSGBench} across a spectrum of ten real-world datasets from diverse domains, utilizing ten advanced TSG methods and twelve evaluation measures. The results highlight the reliability and efficacy of \textsf{TSGBench} in evaluating TSG methods. Crucially, \textsf{TSGBench} delivers a statistical analysis of the performance rankings of these methods, illuminating their varying performance across different datasets and measures and offering nuanced insights into the effectiveness of each method.
Time series generation (TSG) studies have mainly focused on the use of Generative Adversarial Networks (GANs) combined with recurrent neural network (RNN) variants. However, the fundamental limitations and challenges of training GANs still remain. In addition, the RNN-family typically has difficulties with temporal consistency between distant timesteps. Motivated by the successes in the image generation (IMG) domain, we propose TimeVQVAE, the first work, to our knowledge, that uses vector quantization (VQ) techniques to address the TSG problem. Moreover, the priors of the discrete latent spaces are learned with bidirectional transformer models that can better capture global temporal consistency. We also propose VQ modeling in a time-frequency domain, separated into low-frequency (LF) and high-frequency (HF). This allows us to retain important characteristics of the time series and, in turn, generate new synthetic signals that are of better quality, with sharper changes in modularity, than its competing TSG methods. Our experimental evaluation is conducted on all datasets from the UCR archive, using well-established metrics in the IMG literature, such as Fr\'echet inception distance and inception scores. Our implementation on GitHub: \url{https://github.com/ML4ITS/TimeVQVAE}.
We propose causal recurrent variational autoencoder (CR-VAE), a novel generative model that is able to learn a Granger causal graph from a multivariate time series x and incorporates the underlying causal mechanism into its data generation process. Distinct to the classical recurrent VAEs, our CR-VAE uses a multi-head decoder, in which the $p$-th head is responsible for generating the $p$-th dimension of $\mathbf{x}$ (i.e., $\mathbf{x}^p$). By imposing a sparsity-inducing penalty on the weights (of the decoder) and encouraging specific sets of weights to be zero, our CR-VAE learns a sparse adjacency matrix that encodes causal relations between all pairs of variables. Thanks to this causal matrix, our decoder strictly obeys the underlying principles of Granger causality, thereby making the data generating process transparent. We develop a two-stage approach to train the overall objective. Empirically, we evaluate the behavior of our model in synthetic data and two real-world human brain datasets involving, respectively, the electroencephalography (EEG) signals and the functional magnetic resonance imaging (fMRI) data. Our model consistently outperforms state-of-the-art time series generative models both qualitatively and quantitatively. Moreover, it also discovers a faithful causal graph with similar or improved accuracy over existing Granger causality-based causal inference methods. Code of CR-VAE is publicly available at https://github.com/hongmingli1995/CR-VAE.