ICML 2025

Conditional Diffusion Model with Nonlinear Data Transformation for
Time Series Forecasting
J Rishi * 1 GVS Mothish * 1 Deepak Subramani 1
Abstract
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 em-
ploys novel nonlinear transformations and learn-
able conditions in the forward process for time
series forecasting. A new loss formulation for
training is proposed, along with a detailed deriva-
tion of both forward and reverse process. The
new additions improve the diffusion model’s ca-
pacity to capture complex time series patterns,
thus simplifying the reverse process. Our novel
condition facilitates learning an efficient prior dis-
tribution. This also reduces the gap between the
true negative log-likelihood and its variational ap-
proximation. CN-Diff is shown to perform better
than other leading time series models on nine real-
world datasets. Ablation studies are conducted to
elucidate the role of each component of CN-Diff.
1. Introduction
Time series forecasting has become an essential element in
modern data-driven decision-making processes, spanning
a wide range of fields including financial pricing analy-
sis (Kim, 2003), economics (Henrique et al., 2019), trans-
portation planning (Huang et al., 2023), energy (Dumas
et al., 2022) and various other fields (Li et al., 2024a; Rasul
et al., 2022). There has been substantial advancement in
time series modeling, beginning with traditional statistical
techniques such as ARIMA and state-space models, which
initially dominated forecasting efforts. Later, various archi-
tectures of deep neural networks, such as recurrent neural
*Equal contribution 1Department of Computational and Data
Sciences, Indian Institute of Science, Bengaluru, India. Corre-
spondence to: J Rishi <rishij@iisc.ac.in>, GVS Mothish <moth-
ishg@iisc.ac.in>, Deepak Subrama...