Standard IMVC evaluation retrains separate models for different missing-data configurations. We show that this paradigm obscures a fundamental vulnerability: missing rate alone is insufficient to characterize data incompleteness. Specifically, we show that protocols with identical nominal missing rates can differ by up to 50× in their proportion of fully observed samples, inducing drastically different learning regimes. We formalize this phenomenon as incompleteness divergence, providing measures that capture structural disparities across missing-data protocols. We further prove that for a broad class of reconstruction-based objectives, learning becomes structurally ill-posed when the proportion of complete samples falls below a critical threshold, leading to near-random performance. To bypass this theoretical bound, we propose CRAFT (Complete-data Robust Attention-masked Fusion Transformer). CRAFT shifts the burden of robustness from the loss function to the architecture via two key properties: (i) per-sample independence, which removes reliance on complete-sample co-occurrence, and (ii) mask-aware variable-length fusion, which aggregates only observed views through attention masking. This design allows a single model, trained once on complete data, to generalize to diverse missing patterns at inference time without retraining. Extensive experiments on seven benchmarks show that CRAFT matches or outperforms per-configuration baselines while reducing training overhead by 8.8×, demonstrating that robustness to missing data can be achieved as an inherent architectural property. Code (CRAFT) and our imvc-audit toolkit are available at https://anonymous.4open.science/r/CRAFT-BF80/ and https://anonymous.4open.science/r/imvc-audit-8263/.
Diffusion models have emerged as powerful generative approaches for missing-data imputation, yet most existing methods operate directly in data space and degrade when training data are heavily incomplete. We investigate whether shifting diffusion to a learned latent representation improves robustness under missing-completely-at-random (MCAR) corruption. To this end, we propose a two-stage framework: a robust VAE-based imputer first learns compact semantic features from incomplete observations, and a diffusion model is then trained in the resulting latent space. Across training missing rates, we perform a controlled comparison against pixel-space diffusion models under the same incomplete-data setting. The latent diffusion model maintains high sample quality and remains stable up to 50% missingness, while pixel-space diffusion degrades progressively as missingness increases. For downstream imputation, latent diffusion also achieves consistently better performance than pixel-space diffusion. These findings indicate that latent-space modeling mitigates artifact amplification from zero-imputed inputs and provides a more robust generative prior for incomplete-data learning. Overall, our results support latent diffusion as a strong and practically useful alternative to pixel-space diffusion for missing-data problems.
Flow matching assumes fully observed training data, which many real-world applications rarely provide. We propose Missing-Data Flow Matching, which treats the missing coordinates of training samples as latent variables and averages the flow matching loss over the values they could take. We first prove the correction is exact rather than approximate. Under missing completely at random with true completions, the incomplete-data objective equals the complete-data objective, so missingness changes nothing about what flow matching learns and the entire difficulty relocates to the completion model. Our finite-sample analysis then answers design questions that the algorithm leaves open, and the answers are not the ones intuition suggests. Missingness transfers estimator variance rather than adding it, one completion per example already matches complete-data variance exactly, and under a fixed evaluation budget one completion is optimal. A learned completion model contributes a single irreducible bias, which we bound by its expected conditional Wasserstein distance to the true completion law. Experiments numerically validate the theoretical predictions, show that deterministic rather than frozen imputation is what collapses the generated distribution, and place our method alongside strong classical and deep imputation baselines on real tabular data.
Fairoz Nower Khan, Nabuat Zaman Nahim, Peizhong Ju
As real-world prediction systems often face missing modalities at inference, incomplete multimodal learning (IML) remains a practical challenge. While prior methods aim to learn representations robust to missing inputs, representations from incomplete modalities inevitably deviate from their full-modality counterparts due to missing evidence. To explicitly leverage these deviations, we propose MARS (Missingness-Aware Residual-guided Specialization), a mixture-of-experts framework that guides expert specialization based on how representations are reshaped by missingness. By contrasting task representations derived from incomplete inputs with their complete counterparts during training, we derive a privileged residual signal that captures this representational gap. The residual signal guides a residual router to assign samples to experts specialized for the corresponding deviation patterns. In parallel, a feature router learns to imitate this routing behavior using only incomplete inputs, enabling deployment without access to full modalities. To mitigate this train-test router gap, we develop a discrepancy-aware noise regularization that adaptively perturbs the residual router's decisions when the feature router deviates, enhancing expert robustness under imperfect imitation. Experiments on multimodal classification (CASIA-SURF, CREMA-D, UPMC Food-101) and segmentation (MCubeS) under missing scenarios show that MARS consistently surpasses baselines while remaining efficient and extensible to diverse backbones and tasks.