Generating tabular data under conditions is critical to applications requiring precise control over the generative process. Existing methods rely on training-time strategies that do not generalise to unseen constraints during inference, and struggle to handle conditional tasks beyond tabular imputation. While manifold theory offers a principled way to guide generation, current formulations are tied to specific inference-time objectives and are limited to continuous domains. We extend manifold theory to tabular data and expand its scope to handle diverse inference-time objectives. On this foundation, we introduce HARPOON, a tabular diffusion method that guides unconstrained samples along the manifold geometry to satisfy diverse tabular conditions at inference. We validate our theoretical contributions empirically on tasks such as imputation and enforcing inequality constraints, demonstrating HARPOON'S strong performance across diverse datasets and the practical benefits of manifold-aware guidance for tabular data. Code URL: https://github.com/adis98/Harpoon

翻译：在生成过程中需要精确控制的应用中，生成满足条件的表格数据至关重要。现有方法依赖于训练时策略，这些策略无法泛化至推理阶段未见过的约束条件，且难以处理表格填补之外的条件生成任务。虽然流形理论为引导生成提供了原则性方法，但现有公式与特定的推理时目标绑定，且仅限于连续域。本文将流形理论扩展至表格数据，并拓宽其适用范围以处理多样化的推理时目标。在此基础上，我们提出了HARPOON——一种表格扩散方法，该方法沿流形几何引导无约束样本，在推理时满足多样化的表格条件。我们通过填补任务和不等式约束强制执行等任务，实证验证了理论贡献，证明了HARPOON在不同数据集上的优异性能，以及流形感知引导对表格数据的实际优势。代码地址：https://github.com/adis98/Harpoon