# DecoVAE: a Lightweight Interpretable Trend-Seasonal VAE Framework for Efficient Probabilistic Time Series Forecasting

arXiv: https://arxiv.org/abs/2608.20052 · HTML: https://mlsanity.com/paper/2608.20052/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 46 references that are in the map.
- First posted on arXiv 20 Aug 2026.

## Builds on (most cited first, 26 of 26)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [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)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Parallel WaveGAN: A fast waveform generation model based on generative adversarial networks with multi-resolution spectrogram](https://mlsanity.com/paper/1910.11480/) (2019)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2307.11494/) (2023)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [DBLoss: Decomposition-based Loss Function for Time Series Forecasting](https://mlsanity.com/paper/2510.23672/) (2025)
- [Revitalizing Multivariate Time Series Forecasting: Learnable Decomposition with Inter-Series Dependencies and Intra-Series Variations Modeling](https://mlsanity.com/paper/2402.12694/) (2024)
- [Time Series Diffusion in the Frequency Domain](https://mlsanity.com/paper/2402.05933/) (2024)
- [ProbTS: Benchmarking Point and Distributional Forecasting across Diverse Prediction Horizons](https://mlsanity.com/paper/2310.07446/) (2023)
- [xPatch: Dual-Stream Time Series Forecasting with Exponential Seasonal-Trend Decomposition](https://mlsanity.com/paper/2412.17323/) (2024)
- [It's TIME: Towards the Next Generation of Time Series Forecasting Benchmarks](https://mlsanity.com/paper/2602.12147/) (2026)
- [Trajectory Flow Matching with Applications to Clinical Time Series Modeling](https://mlsanity.com/paper/2410.21154/) (2024)
- [Parsimony or Capability? Decomposition Delivers Both in Long-term Time Series Forecasting](https://mlsanity.com/paper/2401.11929/) (2024)
- [WFTNet: Exploiting Global and Local Periodicity in Long-term Time Series Forecasting](https://mlsanity.com/paper/2309.11319/) (2023)
- [Time Series Analysis in Frequency Domain: A Survey of Open Challenges, Opportunities and Benchmarks](https://mlsanity.com/paper/2504.07099/) (2025)
- [Towards Non-Stationary Time Series Forecasting with Temporal Stabilization and Frequency Differencing](https://mlsanity.com/paper/2511.08229/) (2025)
- [K2VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2505.23017/) (2025)
- [DeNOTS: Stable Deep Neural ODEs for Time Series](https://mlsanity.com/paper/2408.08055/) (2024)
- [FreDN: Spectral Disentanglement for Time Series Forecasting via Learnable Frequency Decomposition](https://mlsanity.com/paper/2511.11817/) (2025)

## Abstract (arXiv)

Probabilistic time series forecasting remains challenging, largely because modeling distinct trend and seasonal dynamics requires specialized approaches. Existing methods often fail to capture the unique inner properties of these components, lack interpretability, or suffer from heavy memory and runtime overhead. To address these limitations, we propose DecoVAE, a lightweight interpretable trend-seasonal VAE framework that explicitly decomposes time series into trend and seasonal components by applying domain-specific inductive biases. The trend stream enforces structural smoothness using a differential regularizer on the latent trajectory, analogous to the Hodrick-Prescott filter. Concurrently, the seasonal stream operates in the frequency domain via a complex Gaussian VAE, natively capturing the amplitude and phase of periodic patterns. Extensive evaluations across seven real-world benchmarks show that DecoVAE consistently outperforms strong baselines. It achieves reductions of up to 14.96% in CRPS and 23.30% in NMAE for short-term forecasting, and up to 52.68% and 26.51% for long-term horizons. Crucially, DecoVAE yields these accuracy gains while remaining highly efficient, reducing model weight by up to 93% and accelerating speed by up to 74% compared to the second-best method.