Parallel Complex Diffusion for Scalable Time Series Generation
arXiv:2602.17706v1 Announce Type: new Abstract: Modeling long-range dependencies in time series generation poses a fundamental trade-off between representational capacity and computational efficiency. Traditional temporal diffusion models suffer from local entanglement and the $\mathcal{O}(L^2)$ cost of attention mechanisms. We address these limitations by introducing PaCoDi (Parallel Complex Diffusion), a spectral-native architecture that decouples generative modeling in the frequency domain. PaCoDi fundamentally alters the problem topology: the Fourier Transform acts as a diagonalizing operator, converting locally coupled temporal signals into globally decorrelated spectral components. Theoretically, we prove the Quadrature Forward Diffusion and Conditional Reverse Factorization theorem, demonstrating that the complex diffusion process can be split into independent real and imaginary branches. We bridge the gap between this decoupled theory and data reality using a \textbf{Mean Fiel
arXiv:2602.17706v1 Announce Type: new Abstract: Modeling long-range dependencies in time series generation poses a fundamental trade-off between representational capacity and computational efficiency. Traditional temporal diffusion models suffer from local entanglement and the $\mathcal{O}(L^2)$ cost of attention mechanisms. We address these limitations by introducing PaCoDi (Parallel Complex Diffusion), a spectral-native architecture that decouples generative modeling in the frequency domain. PaCoDi fundamentally alters the problem topology: the Fourier Transform acts as a diagonalizing operator, converting locally coupled temporal signals into globally decorrelated spectral components. Theoretically, we prove the Quadrature Forward Diffusion and Conditional Reverse Factorization theorem, demonstrating that the complex diffusion process can be split into independent real and imaginary branches. We bridge the gap between this decoupled theory and data reality using a \textbf{Mean Field Theory (MFT) approximation} reinforced by an interactive correction mechanism. Furthermore, we generalize this discrete DDPM to continuous-time Frequency SDEs, rigorously deriving the Spectral Wiener Process describe the differential spectral Brownian motion limit. Crucially, PaCoDi exploits the Hermitian Symmetry of real-valued signals to compress the sequence length by half, achieving a 50% reduction in attention FLOPs without information loss. We further derive a rigorous Heteroscedastic Loss to handle the non-isotropic noise distribution on the compressed manifold. Extensive experiments show that PaCoDi outperforms existing baselines in both generation quality and inference speed, offering a theoretically grounded and computationally efficient solution for time series modeling.
Executive Summary
This article introduces PaCoDi, a novel spectral-native architecture for scalable time series generation that decouples generative modeling in the frequency domain. By leveraging the Fourier Transform, PaCoDi converts locally coupled temporal signals into globally decorrelated spectral components, allowing for a significant reduction in computational cost. Theoretically grounded and computationally efficient, PaCoDi outperforms existing baselines in generation quality and inference speed. The authors' rigorous Heteroscedastic Loss and Mean Field Theory approximation further enhance the model's performance. This breakthrough has far-reaching implications for time series modeling and analysis, offering a scalable solution for real-world applications.
Key Points
- ▸ PaCoDi decouples generative modeling in the frequency domain using the Fourier Transform.
- ▸ The model achieves a 50% reduction in attention FLOPs without information loss.
- ▸ PaCoDi is theoretically grounded and computationally efficient, outperforming existing baselines.
Merits
Strength in Theory
The authors provide a rigorous theoretical foundation for PaCoDi, including the Quadrature Forward Diffusion and Conditional Reverse Factorization theorem.
Strength in Computation
PaCoDi achieves a significant reduction in computational cost through its decoupling of generative modeling in the frequency domain.
Strength in Empirical Performance
Extensive experiments demonstrate PaCoDi's superiority over existing baselines in both generation quality and inference speed.
Demerits
Limitation in Generalizability
The authors focus on time series generation, and it remains to be seen whether PaCoDi's benefits extend to other domains.
Limitation in Interpretability
The complex diffusion process and Mean Field Theory approximation may reduce model interpretability, requiring further investigation.
Expert Commentary
PaCoDi represents a significant advancement in the field of time series modeling, offering a theoretically grounded and computationally efficient solution for scalable time series generation. The authors' rigorous Heteroscedastic Loss and Mean Field Theory approximation enhance the model's performance, and the 50% reduction in attention FLOPs without information loss is a notable achievement. While there are limitations in generalizability and interpretability, PaCoDi's breakthrough has far-reaching implications for time series analysis and signal processing. This work will undoubtedly inspire further research in the field, driving innovation and advancement in the application of deep learning to time series data.
Recommendations
- ✓ Future research should focus on extending PaCoDi's benefits to other domains and exploring its applications in areas such as finance, healthcare, and climate modeling.
- ✓ The development of more interpretable and explainable versions of PaCoDi will be essential for its widespread adoption in real-world applications.
