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Missing Data Imputation by Reducing Mutual Information with Rectified Flows
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Proposes MIRI, an iterative missing-data imputation method that reduces mutual information between imputed data and missingness mask by solving an ODE trained with a rectified flow objective, and reports gains in distributional fidelity (MMD) on synthetic, UCI, and CIFAR-10/CelebA imputation.
Problem
Missing data imputation that preserves the data distribution: imputed values should be independent of the missingness mask, which GAN-based and round-robin methods approximate poorly or only heuristically.
Approach
Iteratively minimize the KL divergence between the joint of imputed data and mask and the product of the previous iteration's data marginal and mask marginal; the optimal imputer is an ODE whose velocity field is learned by a rectified flow objective that transports the current imputation to the conditional distribution of missing components given observed ones.
Key results
- On 30% MCAR synthetic data, MIRI achieves MMD 0.036 ± 0.007 versus 0.094 ± 0.018 for HyperImpute, while HyperImpute has lower RMSE (0.862 vs 0.938).
- On CIFAR-10 at 40% missingness, MIRI reaches FID 27.53 versus 65.01 for HyperImpute and PSNR 27.14 versus 23.22.
- On UCI at 40% MCAR, MIRI attains the best mean MMD rank (1.4), ahead of HyperImpute (1.6); under MAR it ranks second (2.0) behind HyperImpute (1.5).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MIRI instead of HyperImpute | CIFAR-10 imputation · 20% missingness | FID: 8.92 -> 6.01 | Helped |
| Use MIRI instead of HyperImpute | CIFAR-10 imputation · 20% missingness | PSNR: 34.09 -> 32.29 | Hurt |
| Use MIRI instead of HyperImpute | CIFAR-10 imputation · 20% missingness | SSIM: 0.9750 -> 0.9736 | Hurt |
| Use MIRI instead of HyperImpute | CIFAR-10 imputation · 40% missingness | FID: 65.01 -> 27.53 | Helped |
| Use MIRI instead of HyperImpute | CIFAR-10 imputation · 40% missingness | PSNR: 23.22 -> 27.14 | Helped |
| Use MIRI instead of HyperImpute | CIFAR-10 imputation · 40% missingness | SSIM: 0.7931 -> 0.9126 | Helped |
| Use MIRI instead of HyperImpute | CIFAR-10 imputation · 60% missingness | FID: 130.36 -> 68.58 | Helped |
| Use MIRI instead of HyperImpute | CIFAR-10 imputation · 60% missingness | PSNR: 20.17 -> 23.22 | Helped |
| Use MIRI instead of HyperImpute | CIFAR-10 imputation · 60% missingness | SSIM: 0.6533 -> 0.8063 | Helped |
| Use MIRI instead of HyperImpute | UCI imputation · 40% missingness, MCAR | mean rank: 1.6 -> 1.4 | Helped |
| Use MIRI instead of HyperImpute | UCI imputation · 40% missingness, MAR | mean rank: 1.5 -> 2.0 | Hurt |
| Use MIRI instead of HyperImpute | UCI imputation · 40% missingness, MNAR | mean rank: 1.6 -> 1.3 | Helped |
Surprising findings
- HyperImpute obtains lower point-wise error (RMSE/MAE) than MIRI on synthetic data, while MIRI wins on distributional MMD.
- MIRI is not best on MAR UCI rankings, where HyperImpute ranks first.
Limitations
- Computationally intensive: each iteration requires training a velocity field and solving an ODE.
- Theory is population-level and ignores finite-sample, optimization, and ODE solver errors.
- Objective targets MCAR/MAR; not designed for MNAR settings.
Experimental setup
Datasets: Synthetic 2D Gaussian mixture UCI regression benchmarks (wine, energy, parkinsons, stock, pumadyn32nm, housing, forest, bike, solar, gas) CIFAR-10 CelebA
Benchmarks: UCI regression benchmarks CIFAR-10 CelebA synthetic 2D Gaussian mixture
Metrics: MMD RMSE MAE FID PSNR SSIM classification accuracy on imputed data mean rank
Baselines: GAIN KnewImp TabCSDI MissDiff HyperImpute TDM MIWAE MICE
Builds on: Rectified Flow GAIN MINE DiffPuter
Closest papers by meaning
- Meta-GAIN for Missing Data Imputation (AAAI 2026 · similarity 0.89)
- McFlow: Monte Carlo Flow Models for Data Imputation (CVPR 2020 · similarity 0.89)
- Rethinking the Diffusion Models for Missing Data Imputation: A Gradient Flow Perspective (NeurIPS 2024 · similarity 0.88)
- Learning What Not to Impute: An Uncertainty-Aware Diffusion Framework for Meaningful Missingness (NeurIPS 2026 · similarity 0.87)
- DiffPuter: Empowering Diffusion Models for Missing Data Imputation (ICLR 2025 · similarity 0.86)
- Distribution Shift in Missing Data Imputation: A Risk-Based Perspective and Importance-Weighted Correction under MAR (NeurIPS 2026 · similarity 0.86)
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