# Sundial: A Family of Highly Capable Time Series Foundation Models

arXiv: https://arxiv.org/abs/2502.00816 · HTML: https://mlsanity.com/paper/2502.00816/

## Key facts

- Cited by 180 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 64 references that are in the map.
- First posted on arXiv 2 Feb 2025.

## Builds on (most cited first, 30 of 48)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Autoregressive Image Generation without Vector Quantization](https://mlsanity.com/paper/2406.11838/) (2024)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)

## Built on by (most cited first, 30 of 180)

- [Chronos-2: From Univariate to Universal Forecasting](https://mlsanity.com/paper/2510.15821/) (2025)
- [TiRex: Zero-Shot Forecasting Across Long and Short Horizons with Enhanced In-Context Learning](https://mlsanity.com/paper/2505.23719/) (2025)
- [Moirai 2.0: When Less Is More for Time Series Forecasting](https://mlsanity.com/paper/2511.11698/) (2025)
- [fev-bench: A Realistic Benchmark for Time Series Forecasting](https://mlsanity.com/paper/2509.26468/) (2025)
- [TS-RAG: Retrieval-Augmented Generation based Time Series Foundation Models are Stronger Zero-Shot Forecaster](https://mlsanity.com/paper/2503.07649/) (2025)
- [It's TIME: Towards the Next Generation of Time Series Forecasting Benchmarks](https://mlsanity.com/paper/2602.12147/) (2026)
- [Aurora: Towards Universal Generative Multimodal Time Series Forecasting](https://mlsanity.com/paper/2509.22295/) (2025)
- [Timer-S1: A Billion-Scale Time Series Foundation Model with Serial Scaling](https://mlsanity.com/paper/2603.04791/) (2026)
- [Kronos: A Foundation Model for the Language of Financial Markets](https://mlsanity.com/paper/2508.02739/) (2025)
- [MIRA: Medical Time Series Foundation Model for Real-World Health Data](https://mlsanity.com/paper/2506.07584/) (2025)
- [Context parroting: A simple but tough-to-beat baseline for foundation models in scientific machine learning](https://mlsanity.com/paper/2505.11349/) (2025)
- [Rethinking Evaluation in the Era of Time Series Foundation Models: (Un)known Information Leakage Challenges](https://mlsanity.com/paper/2510.13654/) (2025)
- [Reverso: Efficient Time Series Foundation Models for Zero-shot Forecasting](https://mlsanity.com/paper/2602.17634/) (2026)
- [TiRex-2: Generalizing TiRex to Multivariate Data and Streaming](https://mlsanity.com/paper/2607.01204/) (2026)
- [TimeMosaic: Temporal Heterogeneity Guided Time Series Forecasting via Adaptive Granularity Patch and Segment-wise Decoding](https://mlsanity.com/paper/2509.19406/) (2025)
- [TS-Reasoner: Aligning Time Series Foundation Models with LLM Reasoning](https://mlsanity.com/paper/2510.03519/) (2025)
- [AlphaCast: A Human Wisdom-LLM Intelligence Co-Reasoning Framework for Interactive Time Series Forecasting](https://mlsanity.com/paper/2511.08947/) (2025)
- [Revisiting the Generic Transformer: Deconstructing a Strong Baseline for Time Series Foundation Models](https://mlsanity.com/paper/2602.06909/) (2026)
- [Towards Foundation Models for Zero-Shot Time Series Anomaly Detection: Leveraging Synthetic Data and Relative Context Discrepancy](https://mlsanity.com/paper/2509.21190/) (2025)
- [Fidel-TS: A High-Fidelity Multimodal Benchmark for Time Series Forecasting](https://mlsanity.com/paper/2509.24789/) (2025)
- [The Forecast After the Forecast: A Post-Processing Shift in Time Series](https://mlsanity.com/paper/2601.20280/) (2026)
- [Falcon-X: A Time Series Foundation Model for Heterogeneous Multivariate Modeling](https://mlsanity.com/paper/2605.27286/) (2026)
- [TimeCopilot](https://mlsanity.com/paper/2509.00616/) (2025)
- [Kairos: Toward Adaptive and Parameter-Efficient Time Series Foundation Models](https://mlsanity.com/paper/2509.25826/) (2025)
- [Pre-trained Forecasting Models: Strong Zero-Shot Feature Extractors for Time Series Classification](https://mlsanity.com/paper/2510.26777/) (2025)
- [Position: Beyond Model-Centric Prediction -- Agentic Time Series Forecasting](https://mlsanity.com/paper/2602.01776/) (2026)
- [Learning the Context of Errors: Black-Box Online Adaptation of Time Series Foundation Models](https://mlsanity.com/paper/2606.14222/) (2026)
- [FlowState: Sampling-Rate-Equivariant Time-Series Forecasting](https://mlsanity.com/paper/2508.05287/) (2025)
- [Xihe: Scalable Zero-Shot Time Series Learner Via Hierarchical Interleaved Block Attention](https://mlsanity.com/paper/2510.21795/) (2025)
- [STAR: Boosting Time Series Foundation Models for Anomaly Detection through State-aware Adapter](https://mlsanity.com/paper/2510.16014/) (2025)

## Abstract (arXiv)

We introduce Sundial, a family of native, flexible, and scalable time series foundation models. To predict the next-patch's distribution, we propose a TimeFlow Loss based on flow-matching, which facilitates native pre-training of Transformers on continuous-valued time series without discrete tokenization. Conditioned on arbitrary-length time series, our models are pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving more flexibility in representation learning than using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with one trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse via TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which achieve unprecedented model capacity and generalization performance. In addition to excellent scalability, Sundial achieves state-of-the-art results on both point and probabilistic forecasting benchmarks with a just-in-time inference speed, i.e., making zero-shot predictions within a few milliseconds. We believe that Sundial's pioneering generative forecasting capability can improve model reliability in real-world decision-making. Code is available at: https://github.com/thuml/Sundial.