Generative modeling has transformed many fields, such as language and visual modeling, while its application in financial markets remains under-explored. As the minimal unit within a financial market is an order, order-flow modeling represents a fundamental generative financial task. However, current approaches often yield unsatisfactory fidelity in generating order flow, and their generation lacks controllability, thereby limiting their practical applications. In this paper, we formulate the challenge of controllable financial market generation, and propose a Diffusion Guided Meta Agent (DigMA) model to address it. Specifically, we employ a conditional diffusion model to capture the dynamics of the market state represented by time-evolving distribution parameters of the mid-price return rate and the order arrival rate, and we define a meta agent with financial economic priors to generate orders from the corresponding distributions. Extensive experimental results show that DigMA achieves superior controllability and generation fidelity. Moreover, we validate its effectiveness as a generative environment for downstream high-frequency trading tasks and its computational efficiency.

Time series generation models are crucial for applications like data augmentation and privacy preservation. Most existing time series generation models are typically designed to generate data from one specified domain. While leveraging data from other domain for better generalization is proved to work in other application areas, this approach remains challenging for time series modeling due to the large divergence in patterns among different real world time series categories. In this paper, we propose a multi-domain time series diffusion model with domain prompts, named TimeDP. In TimeDP, we utilize a time series semantic prototype module which defines time series prototypes to represent time series basis, each prototype vector serving as "word" representing some elementary time series feature. A prototype assignment module is applied to extract the extract domain specific prototype weights, for learning domain prompts as generation condition. During sampling, we extract ``domain prompt" with few-shot samples from the target domain and use the domain prompts as condition to generate time series samples. Experiments demonstrate that our method outperforms baselines to provide the state-of-the-art in-domain generation quality and strong unseen domain generation capability.

Time-series Generation (TSG) is a prominent research area with broad applications in simulations, data augmentation, and counterfactual analysis. While existing methods have shown promise in unconditional single-domain TSG, real-world applications demand for cross-domain approaches capable of controlled generation tailored to domain-specific constraints and instance-level requirements. In this paper, we argue that text can provide semantic insights, domain information and instance-specific temporal patterns, to guide and improve TSG. We introduce “Text-Controlled TSG”, a task focused on generating realistic time series by incorporating textual descriptions. To address data scarcity in this setting, we propose a novel LLM-based Multi-Agent framework that synthesizes diverse, realistic text-to-TS datasets. Furthermore, we introduce Bridge, a hybrid text-controlled TSG framework that integrates semantic prototypes with text description for supporting domain-level guidance. This approach achieves state-of-the-art generation fidelity on 11 of 12 datasets, and improves controllability by up to 12% on MSE and 6% MAE compared to no text input generation, highlighting its potential for generating tailored time-series data.

Synthetic Electronic Health Record (EHR) time-series generation is crucial for advancing clinical machine learning models, as it helps address data scarcity by providing more training data. However, most existing approaches focus primarily on replicating statistical distributions and temporal dependencies of real-world data. We argue that fidelity to observed data alone does not guarantee better model performance, as common patterns may dominate, limiting the representation of rare but important conditions. This highlights the need for generate synthetic samples to improve performance of specific clinical models to fulfill their target outcomes. To address this, we propose TarDiff, a novel target-oriented diffusion framework that integrates task-specific influence guidance into the synthetic data generation process. Unlike conventional approaches that mimic training data distributions, TarDiff optimizes synthetic samples by quantifying their expected contribution to improving downstream model performance through influence functions. Specifically, we measure the reduction in task-specific loss induced by synthetic samples and embed this influence gradient into the reverse diffusion process, thereby steering the generation towards utility-optimized data. Evaluated on six publicly available EHR datasets, TarDiff achieves state-of-the-art performance, outperforming existing methods by up to 20.4% in AUPRC and 18.4% in AUROC. Our results demonstrate that TarDiff not only preserves temporal fidelity but also enhances downstream model performance, offering a robust solution to data scarcity and class imbalance in healthcare analytics.

As one of the most successful generative models, diffusion models have demonstrated remarkable efficacy in synthesizing high-quality images. These models learn the underlying high-dimensional data distribution in an unsupervised manner. Despite their success, diffusion models are highly data-driven and prone to inheriting the imbalances and biases present in real-world data. Some studies have attempted to address these issues by designing text prompts for known biases or using bias labels to construct unbiased data. While these methods have shown improved results, real-world scenarios often contain various unknown biases, and obtaining bias labels is particularly challenging. In this paper, we emphasize the necessity of mitigating bias in pre-trained diffusion models without relying on auxiliary bias annotations. To tackle this problem, we propose a framework, InvDiff, which aims to learn invariant semantic information for diffusion guidance. Specifically, we propose identifying underlying biases in the training data and designing a novel debiasing training objective. Then, we employ a lightweight trainable module that automatically preserves invariant semantic information and uses it to guide the diffusion model's sampling process toward unbiased outcomes simultaneously. Notably, we only need to learn a small number of parameters in the lightweight learnable module without altering the pre-trained diffusion model. Furthermore, we provide a theoretical guarantee that the implementation of InvDiff is equivalent to reducing the error upper bound of generalization. Extensive experimental results on three publicly available benchmarks demonstrate that InvDiff effectively reduces biases while maintaining the quality of image generation. Our code is available at https://github.com/Hundredl/InvDiff.

A unified foundation model for medical time series—pretrained on open access and ethically reviewed medical corpora—offers the potential to reduce annotation burdens, minimize model customization, and enable robust transfer across clinical institutions, modalities, and tasks, particularly in data-scarce or privacy-constrained environments. However, existing time series foundation models struggle to handle medical time series data due to its inherent challenges, including irregular intervals, heterogeneous sampling rates, and frequent missingness. To address these challenges, we introduce MIRA, a unified foundation model specifically designed for medical time series forecasting. MIRA incorporates a Continuous-Time Rotary Positional Encoding that enables fine-grained modeling of variable time intervals, a frequency-specific mixture-of-experts layer that routes computation across latent frequency regimes to further promote temporal specialization, and a Continuous Dynamics Extrapolation Block based on Neural ODE that models the continuous trajectory of latent states, enabling accurate forecasting at arbitrary target timestamps. Pretrained on a large-scale and diverse medical corpus comprising over 454 billion time points collect from publicly available datasets, MIRA achieving reductions in forecasting errors by an average of 8% and 6% in out-of-distribution and in-distribution scenarios, respectively. We also introduce a comprehensive benchmark spanning multiple downstream clinical tasks, establishing a foundation for future research in medical time series modeling.

Recently, diffusion probabilistic models have attracted attention in generative time series forecasting due to their remarkable capacity to generate high-fidelity samples. However, the effective utilization of their strong modeling ability in the probabilistic time series forecasting task remains an open question, partially due to the challenge of instability arising from their stochastic nature. To address this challenge, we introduce a novel Multi-Granularity Time Series Diffusion (MG-TSD) model, which achieves state-of-the-art predictive performance by leveraging the inherent granularity levels within the data as given targets at intermediate diffusion steps to guide the learning process of diffusion models. The way to construct the targets is motivated by the observation that forward process of the diffusion model, which sequentially corrupts the data distribution to a standard normal distribution, intuitively aligns with the process of smoothing fine-grained data into a coarse-grained representation, both of which result in a gradual loss of fine distribution features. In the study, we derive a novel multi-granularity guidance diffusion loss function and propose a concise implementation method to effectively utilize coarse-grained data across various granularity levels. More importantly, our approach does not rely on additional external data, making it versatile and applicable across various domains. Extensive experiments conducted on real-world datasets demonstrate that our MG-TSD model outperforms existing time series prediction methods.