Diffusion Models Beyond Computer Vision: Tabular Data Synthesis, Graph Generation, and Time-Series Forecasting

Abstract—Denoising Diffusion Probabilistic Models (DDPMs) and Score-Based Generative Models have fundamentally transformed continuous image generation and multi-modal synthesis. However, their mathematical extension beyond Euclidean continuous pixel grids into structured enterprise domains—specifically heterogeneous tabular records, non-Euclidean relational graphs, and temporal time-series signals—presents profound structural challenges. Classical generative paradigms, including Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs), suffer from mode collapse, training instability, and poor sample fidelity when modeling mixed-type discrete-continuous marginals, permutation-invariant graph symmetries, and long-horizon autoregressive temporal dependencies. Recently, non-vision diffusion architectures have demonstrated superior mode coverage and exact likelihood estimation across structured data modalities. This paper presents an exhaustive, mathematically formal technical survey and empirical benchmark of modern diffusion models applied to tabular synthesis, topological graph generation, and high-frequency time-series forecasting. We formalize continuous-time Stochastic Differential Equation (SDE) score matching, discrete Markov jump transition kernels for mixed-type categorical variables, and permutation-equivariant Graph Neural Network (GNN) score functions. Furthermore, we construct an enterprise evaluation testbed spanning four mission-critical non-vision datasets (high-dimensional financial fraud tables, molecular bio-graphs, and electrical grid load series). Our empirical findings demonstrate that tabular diffusion architectures achieve a 34.2% reduction in Wasserstein-1 distance over CTGAN, while temporal score-based diffusion improves probabilistic time-series forecasting Continuous Ranked Probability Scores (CRPS) by 28.6% over autoregressive Transformers. Finally, we formulate open challenges in sampling speed acceleration, privacy-preserving differential score perturbation, and combinatorial topological constraints. Index Terms—Diffusion Models, Score-Based Generative Modeling, Tabular Data Synthesis, Graph Generation, Time-Series Forecasting, Stochastic Differential Equations (SDEs), Categorical Markov Chains, Machine Learning.