Chaotic dynamical systems exhibit strong sensitivity to initial conditions and often contain unresolved multiscale processes, making deterministic forecasting fundamentally limited. Generative models offer an appealing alternative by learning distributions over plausible system evolutions; yet, most existing approaches focus on next-step conditional prediction rather than the structure of the underlying dynamics. In this work, we reframe forecasting as a fully generative problem by learning the joint probability distribution of lagged system states over short temporal windows and obtaining forecasts through marginalization. This new perspective allows the model to capture nonlinear temporal dependencies, represent multistep trajectory segments, and produce next-step predictions consistent with the learned joint distribution. We also introduce a general, model-agnostic training and inference framework for joint generative forecasting and show how it enables assessment of forecast robustness and reliability using three complementary uncertainty quantification metrics (ensemble variance, short-horizon autocorrelation, and cumulative Wasserstein drift), without access to ground truth. We evaluate the performance of the proposed method on two canonical chaotic dynamical systems, the Lorenz-63 system and the Kuramoto-Sivashinsky equation, and show that joint generative models yield improved short-term predictive skill, preserve attractor geometry, and achieve substantially more accurate long-range statistical behaviour than conventional conditional next-step models.

翻译：混沌动力系统对初始条件表现出极强的敏感性，且常包含未解析的多尺度过程，这使得确定性预测存在根本性局限性。生成模型通过学习系统可能演化的分布提供了极具吸引力的替代方案；然而，现有方法大多侧重于下一步条件预测，而非底层动力学的结构。在本工作中，我们通过短期时间窗内学习滞后系统状态的联合概率分布，并通过边缘化获得预测，从而将预测重新构建为一个完全生成式问题。这一新视角使模型能够捕捉非线性时间依赖性、表示多步轨迹段，并产生与所学联合分布一致的下一步预测。我们还提出了一个通用的、与模型无关的联合生成式预测训练与推理框架，并展示了如何利用三种互补的不确定性量化指标（集成方差、短时域自相关和累积Wasserstein漂移）在无法获取真实值的情况下评估预测的鲁棒性与可靠性。我们在两个典型混沌动力系统（Lorenz-63系统和Kuramoto-Sivashinsky方程）上评估了所提方法的性能，结果表明：相较于传统的条件式下一步预测模型，联合生成模型能提升短期预测能力、保持吸引子几何结构，并在长期统计行为上实现显著更精确的结果。