Limit Order Book Forecasting with Conditional Diffusion Models

Simulating limit order book (LOB) dynamics is central to market forecasting and evaluation. While diffusion models achieve strong empirical performance, existing approaches lack autoregressive structure and theoretical guarantees. We propose \textbf{LOBGrad}, a conditional DDPM that combines an autoregressive RNN encoder with a diffusion-based generator for probabilistic time-series forecasting. For stationary exponentially mixing transformed LOB sequences with bounded support, we establish an excess-risk oracle inequality for the DDPM noise-prediction objective. In particular, we show how the dependence on the conditioning window can be reduced to the latent-state dimension under contractive dynamics. Experiments on BTC/USDT data show that LOBGrad outperforms diffusion models without an encoder, conditional Wasserstein GANs and statistical baselines on queue metrics, reproduces return distribution and autocorrelation characteristics, and yields well-calibrated probabilistic forecasts across a 20-step horizon.