# ProtoFlow: Prototype-Guided Flow Matching for Multivariate Time Series Forecasting

arXiv: https://arxiv.org/abs/2610.01320 · HTML: https://mlsanity.com/paper/2610.01320/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 33 of its 44 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 33)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [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)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [PDFormer: Propagation Delay-Aware Dynamic Long-Range Transformer for Traffic Flow Prediction](https://mlsanity.com/paper/2301.07945/) (2023)
- [Generalization in Generation: A closer look at Exposure Bias](https://mlsanity.com/paper/1910.00292/) (2019)
- [Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2307.11494/) (2023)
- [Non-autoregressive Conditional Diffusion Models for Time Series Prediction](https://mlsanity.com/paper/2306.05043/) (2023)
- [Vector Quantized Time Series Generation with a Bidirectional Prior Model](https://mlsanity.com/paper/2303.04743/) (2023)
- [Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2410.03024/) (2024)
- [TOTEM: TOkenized Time Series EMbeddings for General Time Series Analysis](https://mlsanity.com/paper/2402.16412/) (2024)
- [TimeDiT: General-purpose Diffusion Transformers for Time Series Foundation Model](https://mlsanity.com/paper/2409.02322/) (2024)
- [MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Process](https://mlsanity.com/paper/2403.05751/) (2024)
- [Non-stationary Diffusion For Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2505.04278/) (2025)
- [The Rise of Diffusion Models in Time-Series Forecasting](https://mlsanity.com/paper/2401.03006/) (2024)
- [TimeDART: A Diffusion Autoregressive Transformer for Self-Supervised Time Series Representation](https://mlsanity.com/paper/2410.05711/) (2024)
- [Vision-Enhanced Time Series Forecasting via Latent Diffusion Models](https://mlsanity.com/paper/2502.14887/) (2025)
- [Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Models](https://mlsanity.com/paper/2503.00951/) (2025)

## Abstract (arXiv)

Generative modeling has shown strong promise for multivariate time mseries (MTS) forecasting, especially scale to high-dimensional settings. Diffusion-based methods achieve competitive performance but typically require many sampling steps at inference. VAE-based non-iterative forecasting frameworks have therefore emerged as an efficient alternative. Within this line of work, vector quantization (VQ) enables controllable latent space modeling by mapping multivariate series into compact discrete representations. Existing VQ-based forecasting methods, however, typically rely on autoregressive (AR) token generation, which suffers from exposure bias and training-inference mismatch. Flow matching provides an efficient non-autoregressive alternative for latent forecasting, but existing formulations usually initialize transport from a generic Gaussian prior. We instead observe that the trained VQ codebook already captures representative latent prototypes and can thus serve as a more informative prior for flow matching. Based on this insight, we propose ProtoFlow, a forecasting framework that combines vector-quantized autoencoding with Prototype-prior Flow matching. Our method first maps multivariate sequences into a discrete latent space, then constructs a structured prior from the learned codebook, and finally learns a DiT-based rectified flow to transport samples from this prior to future latent representations conditioned on historical observations. By replacing generic noise initialization with a learned prototype prior, ProtoFlow avoids the rollout mismatch of AR token prediction and promotes faster training convergence. Extensive experiments on benchmark datasets show that it consistently achieves superior forecasting performance with efficient inference.