Harpoon: Generalised Manifold Guidance for Conditional Tabular Diffusion

2026-02-08

AI Summary

This work proposes a manifold-guided diffusion model that overcomes the limitations of existing conditional generation methods, which often fail to generalize to unseen constraints and are restricted to specific tasks such as imputation. By introducing a manifold geometry–guided mechanism—extended for the first time to tabular data—the method enables flexible conditioning at inference time with arbitrary targets, including inequality constraints, thereby transcending the conventional reliance on continuous domains and fixed conditions. The approach guides unconstrained samples to evolve along the manifold structure of a hybrid discrete-continuous feature space during inference, achieving versatile and general-purpose conditional generation. Experiments demonstrate significant performance gains over baseline methods across diverse tasks, including missing value imputation and inequality-constrained generation, validating the effectiveness and practicality of the proposed manifold-aware guidance.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Diffusion Models for Vision
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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

Problem

• conditional tabular generation
• manifold guidance
• diffusion models
• unseen constraints
• tabular data

Innovation

• manifold guidance
• conditional tabular generation
• diffusion models
• inference-time conditioning
• tabular data