Conditional Diffusion Model with Nonlinear Data Transformation for Time Series Forecasting

Time-series forecasting finds application across domains such as finance, climate science, and energy systems. We introduce the Conditional Diffusion with Nonlinear Data Transformation Model (CN-Diff), a generative framework that employs novel nonlinear transformations and learnable conditions in the forward process for time series forecasting. A new loss formulation for training is proposed, along with a detailed derivation of both forward and reverse process. The new additions improve the diffusion model's capacity to capture complex time series patterns, thus simplifying the reverse process. Our novel condition facilitates learning an efficient prior distribution. This also reduces the gap between the true negative log-likelihood and its variational approximation. CN-Diff is shown to perform better than other leading time series models on nine realworld datasets. Ablation studies are conducted to elucidate the role of each component of CN-Diff.