# Score-CDM: Score-Weighted Convolutional Diffusion Model for Multivariate Time Series Imputation

arXiv: https://arxiv.org/abs/2405.13075 · HTML: https://mlsanity.com/paper/2405.13075/

## Key facts

- Cited by 6 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 32 of its 51 references that are in the map.
- First posted on arXiv 21 May 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 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [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)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [It's Raw! Audio Generation with State-Space Models](https://mlsanity.com/paper/2202.09729/) (2022)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting](https://mlsanity.com/paper/1905.03806/) (2019)
- [An Attention Free Transformer](https://mlsanity.com/paper/2105.14103/) (2021)
- [Inception Transformer](https://mlsanity.com/paper/2205.12956/) (2022)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [Non-autoregressive Conditional Diffusion Models for Time Series Prediction](https://mlsanity.com/paper/2306.05043/) (2023)
- [PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation](https://mlsanity.com/paper/2302.09746/) (2023)

## Built on by (most cited first, 6 of 6)

- [Unraveling Spatio-Temporal Foundation Models via the Pipeline Lens: A Comprehensive Review](https://mlsanity.com/paper/2506.01364/) (2025)
- [FreshRetailNet-50K: A Stockout-Annotated Censored Demand Dataset for Latent Demand Recovery and Forecasting in Fresh Retail](https://mlsanity.com/paper/2505.16319/) (2025)
- [STAMImputer: Spatio-Temporal Attention MoE for Traffic Data Imputation](https://mlsanity.com/paper/2506.08054/) (2025)
- [How to Unlock Time Series Editing? Diffusion-Driven Approach with Multi-Grained Control](https://mlsanity.com/paper/2506.05276/) (2025)
- [LLMs Meet Cross-Modal Time Series Analytics: Overview and Directions](https://mlsanity.com/paper/2507.10620/) (2025)
- [Lossless Compression: A New Benchmark for Time Series Model Evaluation](https://mlsanity.com/paper/2509.21002/) (2025)

## Abstract (arXiv)

Multivariant time series (MTS) data are usually incomplete in real scenarios, and imputing the incomplete MTS is practically important to facilitate various time series mining tasks. Recently, diffusion model-based MTS imputation methods have achieved promising results by utilizing CNN or attention mechanisms for temporal feature learning. However, it is hard to adaptively trade off the diverse effects of local and global temporal features by simply combining CNN and attention. To address this issue, we propose a Score-weighted Convolutional Diffusion Model (Score-CDM for short), whose backbone consists of a Score-weighted Convolution Module (SCM) and an Adaptive Reception Module (ARM). SCM adopts a score map to capture the global temporal features in the time domain, while ARM uses a Spectral2Time Window Block (S2TWB) to convolve the local time series data in the spectral domain. Benefiting from the time convolution properties of Fast Fourier Transformation, ARM can adaptively change the receptive field of the score map, and thus effectively balance the local and global temporal features. We conduct extensive evaluations on three real MTS datasets of different domains, and the result verifies the effectiveness of the proposed Score-CDM.