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MissHDD: Hybrid Deterministic Diffusion for Hetrogeneous Incomplete Data Imputation

Youran Zhou, Mohamed Reda Bouadjenek, Sunil Aryal

TL;DR

MissHDD addresses the challenge of imputing heterogeneous incomplete tabular data by introducing a hybrid two-channel diffusion framework. A continuous DDIM-based channel efficiently denoises numerical variables deterministically, while a discrete latent-path (loopholing) diffusion channel models categorical and discrete variables within their valid simplex manifolds. Both channels share conditioning on observed data and are trained with a self-masking strategy that enables learning directly from incomplete data, optimizing a unified conditional objective p(x^{mis} | x^{obs}). Empirical results show state-of-the-art imputation accuracy, reduced sampling variance, and faster, deterministic inference across MCAR, MAR, and MNAR settings, underscoring the value of structure-aware diffusion for mixed-type tabular data.

Abstract

Incomplete data are common in real-world tabular applications, where numerical, categorical, and discrete attributes coexist within a single dataset. This heterogeneous structure presents significant challenges for existing diffusion-based imputation models, which typically assume a homogeneous feature space and rely on stochastic denoising trajectories. Such assumptions make it difficult to maintain conditional consistency, and they often lead to information collapse for categorical variables or instability when numerical variables require deterministic updates. These limitations indicate that a single diffusion process is insufficient for mixed-type tabular imputation. We propose a hybrid deterministic diffusion framework that separates heterogeneous features into two complementary generative channels. A continuous DDIM-based channel provides efficient and stable deterministic denoising for numerical variables, while a discrete latent-path diffusion channel, inspired by loopholing-based discrete diffusion, models categorical and discrete features without leaving their valid sample manifolds. The two channels are trained under a unified conditional imputation objective, enabling coherent reconstruction of mixed-type incomplete data. Extensive experiments on multiple real-world datasets show that the proposed framework achieves higher imputation accuracy, more stable sampling trajectories, and improved robustness across MCAR, MAR, and MNAR settings compared with existing diffusion-based and classical methods. These results demonstrate the importance of structure-aware diffusion processes for advancing deep learning approaches to incomplete tabular data.

MissHDD: Hybrid Deterministic Diffusion for Hetrogeneous Incomplete Data Imputation

TL;DR

MissHDD addresses the challenge of imputing heterogeneous incomplete tabular data by introducing a hybrid two-channel diffusion framework. A continuous DDIM-based channel efficiently denoises numerical variables deterministically, while a discrete latent-path (loopholing) diffusion channel models categorical and discrete variables within their valid simplex manifolds. Both channels share conditioning on observed data and are trained with a self-masking strategy that enables learning directly from incomplete data, optimizing a unified conditional objective p(x^{mis} | x^{obs}). Empirical results show state-of-the-art imputation accuracy, reduced sampling variance, and faster, deterministic inference across MCAR, MAR, and MNAR settings, underscoring the value of structure-aware diffusion for mixed-type tabular data.

Abstract

Incomplete data are common in real-world tabular applications, where numerical, categorical, and discrete attributes coexist within a single dataset. This heterogeneous structure presents significant challenges for existing diffusion-based imputation models, which typically assume a homogeneous feature space and rely on stochastic denoising trajectories. Such assumptions make it difficult to maintain conditional consistency, and they often lead to information collapse for categorical variables or instability when numerical variables require deterministic updates. These limitations indicate that a single diffusion process is insufficient for mixed-type tabular imputation. We propose a hybrid deterministic diffusion framework that separates heterogeneous features into two complementary generative channels. A continuous DDIM-based channel provides efficient and stable deterministic denoising for numerical variables, while a discrete latent-path diffusion channel, inspired by loopholing-based discrete diffusion, models categorical and discrete features without leaving their valid sample manifolds. The two channels are trained under a unified conditional imputation objective, enabling coherent reconstruction of mixed-type incomplete data. Extensive experiments on multiple real-world datasets show that the proposed framework achieves higher imputation accuracy, more stable sampling trajectories, and improved robustness across MCAR, MAR, and MNAR settings compared with existing diffusion-based and classical methods. These results demonstrate the importance of structure-aware diffusion processes for advancing deep learning approaches to incomplete tabular data.

Paper Structure

This paper contains 56 sections, 40 equations, 4 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Heterogeneous Feature Types in Tabular Data
  5. Training with Incomplete Tabular Data
  6. Missing Completely at Random (MCAR)
  7. Missing At Random (MAR)
  8. Missing Not At Random (MNAR)
  9. Denoising Diffusion Probabilistic Models
  10. Forward diffusion
  11. Reverse denoising process
  12. Training objective
  13. Limitations for imputation
  14. The Proposed MissHDD Framework
  15. Channel 1: Conditional DDIM for Efficient Continuous Variable Imputation
  16. ...and 41 more sections

Figures (4)

  • Figure 1: Overview of the MissHDD framework. Continuous and categorical and discrete features are separated and imputed through two diffusion channels: a conditional deterministic DDIM for continuous variables (Channel 1) and a Loopholing-based discrete diffusion model for categorical and discrete variables (Channel 2). categorical and discrete inputs are represented using one-hot encoding, while integer index embeddings are also supported. Both channels are trained with a self-masking strategy, and the reconstructed outputs are decoded and merged to form the final imputed table.
  • Figure 2: Self-masking strategy used in MissHDD. During training, a portion of observed entries is randomly masked to create pseudo-missing targets. The remaining entries serve as conditioning information for both the continuous and discrete diffusion channels.
  • Figure 3: Imputation accuracy comparison under three missingness mechanisms: MCAR, MAR, and MNAR. Each subplot visualizes dataset-wise AvgErr (left panel) and aggregated summary statistics (boxplot, right panel) across varying missing rates.
  • Figure 4: RMSE Comparison with varying $\eta$ values.