# Conditional Denoising Meets Polynomial Modeling: A Flexible Decoupled Framework for Time Series Forecasting

arXiv: https://arxiv.org/abs/2410.13253 · HTML: https://mlsanity.com/paper/2410.13253/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 31 of its 56 references that are in the map.
- First posted on arXiv 17 Oct 2024.

## 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 31)

- [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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [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)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [TSMixer: Lightweight MLP-Mixer Model for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2306.09364/) (2023)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement](https://mlsanity.com/paper/2301.03028/) (2023)
- [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)
- [SegRNN: Segment Recurrent Neural Network for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2308.11200/) (2023)
- [Machine Learning Advances for Time Series Forecasting](https://mlsanity.com/paper/2012.12802/) (2020)
- [Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusion](https://mlsanity.com/paper/2211.02590/) (2022)
- [ConvTimeNet: A Deep Hierarchical Fully Convolutional Model for Multivariate Time Series Analysis](https://mlsanity.com/paper/2403.01493/) (2024)
- [PatchMixer: A Patch-Mixing Architecture for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2310.00655/) (2023)
- [Generative Pretrained Hierarchical Transformer for Time Series Forecasting](https://mlsanity.com/paper/2402.16516/) (2024)
- [DiffSTOCK: Probabilistic relational Stock Market Predictions using Diffusion Models](https://mlsanity.com/paper/2403.14063/) (2024)

## Built on by (most cited first, 3 of 3)

- [StaTS: Spectral Trajectory Schedule Learning for Adaptive Time Series Forecasting with Frequency Guided Denoiser](https://mlsanity.com/paper/2603.00037/) (2026)
- [CoGenCast: A Coupled Autoregressive-Flow Generative Framework for Time Series Forecasting](https://mlsanity.com/paper/2602.03564/) (2026)
- [Differencing the Diffusion Trajectory toward Uncertain Components for Time Series Forecasting](https://mlsanity.com/paper/2607.22599/) (2026)

## Abstract (arXiv)

Time series forecasting models are becoming increasingly prevalent due to their critical role in decision-making across various domains. However, most existing approaches represent the coupled temporal patterns, often neglecting the distinction between their specific components. In particular, fluctuating patterns and smooth trends within time series exhibit distinct characteristics. In this work, to model complicated temporal patterns, we propose a Conditional Denoising Polynomial Modeling (CDPM) framework, where probabilistic diffusion models and deterministic linear models are trained end-to-end. Instead of modeling the coupled time series, CDPM decomposes it into trend and seasonal components for modeling them separately. To capture the fluctuating seasonal component, we employ a probabilistic diffusion model based on statistical properties from the historical window. For the smooth trend component, a module is proposed to enhance linear models by incorporating historical dependencies, thereby preserving underlying trends and mitigating noise distortion. Extensive experiments conducted on six benchmarks demonstrate the effectiveness of our framework, highlighting the potential of combining probabilistic and deterministic models. Our code is available at https://github.com/zjt-gpu/CDPM.