Generating the Term Structure of Interest Rates with Diffusion Models

This study introduces a novel generative modeling framework for simulating the term structure of interest rates. In recent years, generative models have achieved significant progress in image generation and are increasingly being applied to finance. To the best of our knowledge, this is the first study to apply a generative model―specifically, a diffusion model―to the term structure of interest rates. Furthermore, we extend the framework to incorporate conditional generation mechanisms and v-parameterization. The training dataset consists of spot yield curves constructed from daily overnight index swap (OIS) rates using cubic Hermite splines. As base conditioning variables, we use short-term interest rates and changes in consumer price indexes (CPIs). Empirical analysis covering the period from 2015 to 2025 demonstrates that our model successfully reproduces the level and shape of yield curves corresponding to historical macroeconomic conditions and short-term interest rate environments. Additionally, when incorporating further conditioning variables related to quantitative easing policies, monetary base, current account balances, and nominal gross domestic product (GDP), we find that the inclusion of quantitative easing indicator notably enhances the model’s output relative to the base conditioning case. This suggests improved robustness and representational capacity under expanded conditioning. In consideration of practical applications, we further analyze the generation outcomes derived from difference-based learning, confirming that the performance of out-of-sample generation is comparable to that of direct generation. Moreover, we also examine an alternative approach based on factor models commonly used in finance and macroeconomics to estimate the functional form of yield curves. Specifically, we consider the Nelson–Siegel–Svensson (NSS) model and investigate the indirect generation of synthetic yield curves by producing the NSS model’s latent factors. Compared to direct generation, this factor-based indirect method enables faster generation while still achieving comparable reproducibility in terms of both the level and the shape of the yield curves.