Diffusion Models

Diffolio: A Diffusion Model for Multivariate Probabilistic Financial Time-Series Forecasting and Portfolio Construction ArXiv ID: 2511.07014 “View on arXiv” Authors: So-Yoon Cho, Jin-Young Kim, Kayoung Ban, Hyeng Keun Koo, Hyun-Gyoon Kim Abstract Probabilistic forecasting is crucial in multivariate financial time-series for constructing efficient portfolios that account for complex cross-sectional dependencies. In this paper, we propose Diffolio, a diffusion model designed for multivariate financial time-series forecasting and portfolio construction. Diffolio employs a denoising network with a hierarchical attention architecture, comprising both asset-level and market-level layers. Furthermore, to better reflect cross-sectional correlations, we introduce a correlation-guided regularizer informed by a stable estimate of the target correlation matrix. This structure effectively extracts salient features not only from historical returns but also from asset-specific and systematic covariates, significantly enhancing the performance of forecasts and portfolios. Experimental results on the daily excess returns of 12 industry portfolios show that Diffolio outperforms various probabilistic forecasting baselines in multivariate forecasting accuracy and portfolio performance. Moreover, in portfolio experiments, portfolios constructed from Diffolio’s forecasts show consistently robust performance, thereby outperforming those from benchmarks by achieving higher Sharpe ratios for the mean-variance tangency portfolio and higher certainty equivalents for the growth-optimal portfolio. These results demonstrate the superiority of our proposed Diffolio in terms of not only statistical accuracy but also economic significance. ...

Forecasting implied volatility surface with generative diffusion models ArXiv ID: 2511.07571 “View on arXiv” Authors: Chen Jin, Ankush Agarwal Abstract We introduce a conditional Denoising Diffusion Probabilistic Model (DDPM) for generating arbitrage-free implied volatility (IV) surfaces, offering a more stable and accurate alternative to existing GAN-based approaches. To capture the path-dependent nature of volatility dynamics, our model is conditioned on a rich set of market variables, including exponential weighted moving averages (EWMAs) of historical surfaces, returns and squared returns of underlying asset, and scalar risk indicators like VIX. Empirical results demonstrate our model significantly outperforms leading GAN-based models in capturing the stylized facts of IV dynamics. A key challenge is that historical data often contains small arbitrage opportunities in the earlier dataset for training, which conflicts with the goal of generating arbitrage-free surfaces. We address this by incorporating a standard arbitrage penalty into the loss function, but apply it using a novel, parameter-free weighting scheme based on the signal-to-noise ratio (SNR) that dynamically adjusts the penalty’s strength across the diffusion process. We also show a formal analysis of this trade-off and provide a proof of convergence showing that the penalty introduces a small, controllable bias that steers the model toward the manifold of arbitrage-free surfaces while ensuring the generated distribution remains close to the real-world data. ...

Multi-Agent Regime-Conditioned Diffusion (MARCD) for CVaR-Constrained Portfolio Decisions ArXiv ID: 2510.10807 “View on arXiv” Authors: Ali Atiah Alzahrani Abstract We examine whether regime-conditioned generative scenarios combined with a convex CVaR allocator improve portfolio decisions under regime shifts. We present MARCD, a generative-to-decision framework with: (i) a Gaussian HMM to infer latent regimes; (ii) a diffusion generator that produces regime-conditioned scenarios; (iii) signal extraction via blended, shrunk moments; and (iv) a governed CVaR epigraph quadratic program. Contributions: Within the Scenario stage we introduce a tail-weighted diffusion objective that up-weights low-quantile outcomes relevant for drawdowns and a regime-expert (MoE) denoiser whose gate increases with crisis posteriors; both are evaluated end-to-end through the allocator. Under strict walk-forward on liquid multi-asset ETFs (2005-2025), MARCD exhibits stronger scenario calibration and materially smaller drawdowns: MaxDD 9.3% versus 14.1% for BL (a 34% reduction) over 2020-2025 out-of-sample. The framework provides an auditable pipeline with explicit budget, box, and turnover constraints, demonstrating the value of decision-aware generative modeling in finance. ...

Painting the market: generative diffusion models for financial limit order book simulation and forecasting ArXiv ID: 2509.05107 “View on arXiv” Authors: Alfred Backhouse, Kang Li, Jakob Foerster, Anisoara Calinescu, Stefan Zohren Abstract Simulating limit order books (LOBs) has important applications across forecasting and backtesting for financial market data. However, deep generative models struggle in this context due to the high noise and complexity of the data. Previous work uses autoregressive models, although these experience error accumulation over longer-time sequences. We introduce a novel approach, converting LOB data into a structured image format, and applying diffusion models with inpainting to generate future LOB states. This method leverages spatio-temporal inductive biases in the order book and enables parallel generation of long sequences overcoming issues with error accumulation. We also publicly contribute to LOB-Bench, the industry benchmark for LOB generative models, to allow fair comparison between models using Level-2 and Level-3 order book data (with or without message level data respectively). We show that our model achieves state-of-the-art performance on LOB-Bench, despite using lower fidelity data as input. We also show that our method prioritises coherent global structures over local, high-fidelity details, providing significant improvements over existing methods on certain metrics. Overall, our method lays a strong foundation for future research into generative diffusion approaches to LOB modelling. ...

DiffVolume: Diffusion Models for Volume Generation in Limit Order Books ArXiv ID: 2508.08698 “View on arXiv” Authors: Zhuohan Wang, Carmine Ventre Abstract Modeling limit order books (LOBs) dynamics is a fundamental problem in market microstructure research. In particular, generating high-dimensional volume snapshots with strong temporal and liquidity-dependent patterns remains a challenging task, despite recent work exploring the application of Generative Adversarial Networks to LOBs. In this work, we propose a conditional \textbf{“Diff”}usion model for the generation of future LOB \textbf{“Volume”} snapshots (\textbf{“DiffVolume”}). We evaluate our model across three axes: (1) \textit{“Realism”}, where we show that DiffVolume, conditioned on past volume history and time of day, better reproduces statistical properties such as marginal distribution, spatial correlation, and autocorrelation decay; (2) \textit{“Counterfactual generation”}, allowing for controllable generation under hypothetical liquidity scenarios by additionally conditioning on a target future liquidity profile; and (3) \textit{“Downstream prediction”}, where we show that the synthetic counterfactual data from our model improves the performance of future liquidity forecasting models. Together, these results suggest that DiffVolume provides a powerful and flexible framework for realistic and controllable LOB volume generation. ...

Solving dynamic portfolio selection problems via score-based diffusion models ArXiv ID: 2507.09916 “View on arXiv” Authors: Ahmad Aghapour, Erhan Bayraktar, Fengyi Yuan Abstract In this paper, we tackle the dynamic mean-variance portfolio selection problem in a {"\it model-free"} manner, based on (generative) diffusion models. We propose using data sampled from the real model $\mathbb P$ (which is unknown) with limited size to train a generative model $\mathbb Q$ (from which we can easily and adequately sample). With adaptive training and sampling methods that are tailor-made for time series data, we obtain quantification bounds between $\mathbb P$ and $\mathbb Q$ in terms of the adapted Wasserstein metric $\mathcal A W_2$. Importantly, the proposed adapted sampling method also facilitates {"\it conditional sampling"}. In the second part of this paper, we provide the stability of the mean-variance portfolio optimization problems in $\mathcal A W _2$. Then, combined with the error bounds and the stability result, we propose a policy gradient algorithm based on the generative environment, in which our innovative adapted sampling method provides approximate scenario generators. We illustrate the performance of our algorithm on both simulated and real data. For real data, the algorithm based on the generative environment produces portfolios that beat several important baselines, including the Markowitz portfolio, the equal weight (naive) portfolio, and S&P 500. ...

Diffusion Factor Models: Generating High-Dimensional Returns with Factor Structure ArXiv ID: 2504.06566 “View on arXiv” Authors: Unknown Abstract Financial scenario simulation is essential for risk management and portfolio optimization, yet it remains challenging especially in high-dimensional and small data settings common in finance. We propose a diffusion factor model that integrates latent factor structure into generative diffusion processes, bridging econometrics with modern generative AI to address the challenges of the curse of dimensionality and data scarcity in financial simulation. By exploiting the low-dimensional factor structure inherent in asset returns, we decompose the score function–a key component in diffusion models–using time-varying orthogonal projections, and this decomposition is incorporated into the design of neural network architectures. We derive rigorous statistical guarantees, establishing nonasymptotic error bounds for both score estimation at O(d^{“5/2”} n^{"-2/(k+5)"}) and generated distribution at O(d^{“5/4”} n^{"-1/2(k+5)"}), primarily driven by the intrinsic factor dimension k rather than the number of assets d, surpassing the dimension-dependent limits in the classical nonparametric statistics literature and making the framework viable for markets with thousands of assets. Numerical studies confirm superior performance in latent subspace recovery under small data regimes. Empirical analysis demonstrates the economic significance of our framework in constructing mean-variance optimal portfolios and factor portfolios. This work presents the first theoretical integration of factor structure with diffusion models, offering a principled approach for high-dimensional financial simulation with limited data. Our code is available at https://github.com/xymmmm00/diffusion_factor_model. ...

Financial Wind Tunnel: A Retrieval-Augmented Market Simulator ArXiv ID: 2503.17909 “View on arXiv” Authors: Unknown Abstract Market simulator tries to create high-quality synthetic financial data that mimics real-world market dynamics, which is crucial for model development and robust assessment. Despite continuous advancements in simulation methodologies, market fluctuations vary in terms of scale and sources, but existing frameworks often excel in only specific tasks. To address this challenge, we propose Financial Wind Tunnel (FWT), a retrieval-augmented market simulator designed to generate controllable, reasonable, and adaptable market dynamics for model testing. FWT offers a more comprehensive and systematic generative capability across different data frequencies. By leveraging a retrieval method to discover cross-sectional information as the augmented condition, our diffusion-based simulator seamlessly integrates both macro- and micro-level market patterns. Furthermore, our framework allows the simulation to be controlled with wide applicability, including causal generation through “what-if” prompts or unprecedented cross-market trend synthesis. Additionally, we develop an automated optimizer for downstream quantitative models, using stress testing of simulated scenarios via FWT to enhance returns while controlling risks. Experimental results demonstrate that our approach enables the generalizable and reliable market simulation, significantly improve the performance and adaptability of downstream models, particularly in highly complex and volatile market conditions. Our code and data sample is available at https://anonymous.4open.science/r/fwt_-E852 ...

Federated Diffusion Modeling with Differential Privacy for Tabular Data Synthesis ArXiv ID: 2412.16083 “View on arXiv” Authors: Unknown Abstract The increasing demand for privacy-preserving data analytics in various domains necessitates solutions for synthetic data generation that rigorously uphold privacy standards. We introduce the DP-FedTabDiff framework, a novel integration of Differential Privacy, Federated Learning and Denoising Diffusion Probabilistic Models designed to generate high-fidelity synthetic tabular data. This framework ensures compliance with privacy regulations while maintaining data utility. We demonstrate the effectiveness of DP-FedTabDiff on multiple real-world mixed-type tabular datasets, achieving significant improvements in privacy guarantees without compromising data quality. Our empirical evaluations reveal the optimal trade-offs between privacy budgets, client configurations, and federated optimization strategies. The results affirm the potential of DP-FedTabDiff to enable secure data sharing and analytics in highly regulated domains, paving the way for further advances in federated learning and privacy-preserving data synthesis. ...

Limit Order Book Event Stream Prediction with Diffusion Model ArXiv ID: 2412.09631 “View on arXiv” Authors: Unknown Abstract Limit order book (LOB) is a dynamic, event-driven system that records real-time market demand and supply for a financial asset in a stream flow. Event stream prediction in LOB refers to forecasting both the timing and the type of events. The challenge lies in modeling the time-event distribution to capture the interdependence between time and event type, which has traditionally relied on stochastic point processes. However, modeling complex market dynamics using stochastic processes, e.g., Hawke stochastic process, can be simplistic and struggle to capture the evolution of market dynamics. In this study, we present LOBDIF (LOB event stream prediction with diffusion model), which offers a new paradigm for event stream prediction within the LOB system. LOBDIF learns the complex time-event distribution by leveraging a diffusion model, which decomposes the time-event distribution into sequential steps, with each step represented by a Gaussian distribution. Additionally, we propose a denoising network and a skip-step sampling strategy. The former facilitates effective learning of time-event interdependence, while the latter accelerates the sampling process during inference. By introducing a diffusion model, our approach breaks away from traditional modeling paradigms, offering novel insights and providing an effective and efficient solution for learning the time-event distribution in order streams within the LOB system. Extensive experiments using real-world data from the limit order books of three widely traded assets confirm that LOBDIF significantly outperforms current state-of-the-art methods. ...