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.

Integrating multimodal datasets in clinical oncology is frequently hindered by high dimensionality and blockwise missingness, where entire data sources are unavailable for specific patient subsets. Standard survival models often struggle with these gaps, leading to biased results or patient exclusion. We introduce Multimodality Stacking with Blockwise missing values (MSB), a late-fusion framework for survival analysis that independently models modality-specific features before aggregating predictions via a cross-validated stacking meta-learner. MSB was validated on the PIONeeR study (n=443 patients, 378 biomarkers across eight heterogeneous sources) to predict progression-free survival in advanced non-small cell lung cancer patients receiving immunotherapy. MSB yielded higher predictive performance (C-index) than baseline algorithms. Improvements varied by baseline strength: linear models showed a 15.9% increase (p<0.001 for the Wilcoxon signed-rank test), random survival forests gained 5.4% (p=0.002), and gradient boosting methods improved by 2.1% (p=0.030). Beyond discrimination, MSB reduced the generalization gap (train-test difference in 5 folds cross-validation repeated 3 times: 0.055 vs 0.380 for linear models). Permutation importance analysis identified routine laboratory markers, clinical features, and PD-L1 expression as primary predictive drivers. Missing block indicators showed negligible importance, suggesting the model learned from biomarker values rather than data availability patterns. MSB provides a statistically validated framework for multimodal survival prediction with blockwise missingness. By enabling systematic biomarker evaluation without requiring complete data, MSB offers a practical tool for predictive modeling in biomedical research, pending external validation. Implementation is available at https://github.com/MohamedBoussena/MSB under Inria license.

Stochastic gradient methods are central to modern large-scale learning, but their use with incomplete covariates remains delicate since imputation schemes generally introduce systematic gradient biases, as shown for linear models. In this work, we prove that all parametric models exhibit similar gradient bias for various imputation procedures and characterize exactly the dependence on the missingness ratio vector $p$, with $O(\|p\|)$ as the leading term. We exploit this analysis to propose a simple debiasing procedure for stochastic gradient descent (SGD) with missing values based on Richardson extrapolation, which leverages the exact expression of the gradient bias. The key idea is to \emph{deliberately add missingness}: from an already incomplete observation, we generate a further-thinned version at a higher, controlled missingness level, and combine the two resulting stochastic gradients to cancel the leading bias term. We prove that one Richardson step reduces the gradient bias from $O(\|p\|)$ to $O(\|p\|^2)$ under several missingness scenarios. Our proposed method is computationally efficient, model-agnostic and applies to any parametric loss whose stochastic gradient can be computed after imputation. Furthermore, when missing indicators are independent, the population gradient bias is a multilinear polynomial in $p$ and depends only on population gradient errors induced by declaring a single coordinate missing. In this case, our method generalizes to a multi-step Richardson procedure which recursively cancels higher-order terms. Empirically, Richardson debiasing improves optimization and estimation across several generalized linear models and combines positively with widely used imputation procedures such as MICE. These results suggest that, somewhat counter-intuitively, adding controlled missingness on top of existing missing data can make stochastic learning from incomplete data more accurate.

Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift. To bridge this gap, we present Latent Laplace Diffusion (LLapDiff), a generative framework that models the target as a low-dimensional latent trajectory, enabling horizon-wide generation without step-by-step integration over physical time. We guide the reverse process utilizing a stable modal parameterization motivated by stochastic port-Hamiltonian dynamics, and parameterize its mean evolution in the Laplace domain via learnable complex-conjugate poles, enabling direct evaluation over irregular timestamps. We also link continuous dynamics to irregular observations through renewal-averaging analysis, which maps sampling gaps to effective event-domain poles and motivates a gap-aware history summarizer. Extensive experiments show that LLapDiff improves over baselines in long-horizon forecasting, and its continuous-time generative nature supports missing-value imputation by querying the same model at historical timestamps. Code is available at https://github.com/pixelhero98/LLapDiffusion.

Large language models (LLMs) are increasingly deployed in settings where the available context is incomplete or degraded. We argue that an LLM generating answers under incomplete context can be viewed as an implicit imputer, and evaluated against a criterion from the multiple imputation (MI) literature: uncertainty should scale with the amount of missing information. We assess this criterion on SQuAD, using a controlled framework in which context availability is varied across five levels. We evaluate two answer-level uncertainty measures that can be estimated from repeated sampling: sampling-based confidence (empirical mode frequency) and response entropy. Confidence fails to reflect increasing missingness: it remains high even as accuracy collapses. Entropy, by contrast, increases with context removal, consistent with the MI analogy, and explains substantially more variance in accuracy than confidence across all evidence levels (quadratic $R^2$ gap up to 0.057). We further introduce a black-box diagnostic $ρ_R(α)$ that estimates the proportion of baseline uncertainty resolved by context level $α$, requiring only repeated sampling with and without context. These results suggest that entropy is a more responsive black-box uncertainty measure than confidence under incomplete context.

Order-Agnostic autoregressive models have demonstrated strong performance in deep generative modeling, yet their use in settings with incomplete data remains largely unexplored. In this work, we reinterpret them through the lens of missing data. First, we show that their standard training procedure on fully observed data implicitly performs imputation under a missing completely at random mechanism, resulting in robust out-of-sample imputation performance in settings with high missingness. Second, we introduce the first principled framework for training them directly on incomplete datasets under general missingness mechanisms. Third, we leverage their amortized conditional density estimation to perform active information acquisition, i.e., sequentially selecting the most informative missing variables for downstream prediction or inference. Across a suite of real-world benchmarks, our Missingness-Aware Order-Agnostic Autoregressive Model (MO-ARM) consistently outperforms established imputation baselines.

The standard constraint-based paradigm for causal discovery with incomplete data -- impute first, test second -- is frequently miscalibrated: any consistent conditional independence (CI) test rejects a true null with probability approaching 1 when imputation error induces spurious conditional dependence. We introduce PAIR-CI, a nonparametric CI test that restores calibration by integrating multiple imputation directly into the inferential procedure via a paired permutation design. PAIR-CI compares cross-validated models that include and exclude the candidate variable while receiving the same imputed conditioning set, forcing imputation error to cancel in their loss difference rather than contaminate the test statistic. A provably consistent variance estimator jointly accounts for uncertainty arising from cross-validation and multiple imputation -- to our knowledge, the first formal unification of these two inferential frameworks. In simulations, existing imputation-based CI tests exhibit false positive rates of 28--45% when data are missing not at random (MNAR), whereas PAIR-CI averages below the nominal 5% level across data-generating processes and missingness mechanisms. These gains are largest in nonlinear settings and grow with causal graph size: when integrated into the PC algorithm, PAIR-CI reduces structural Hamming distance by 8% on 10-variable nonlinear graphs, 15% on 30-variable equivalents, and up to 44% on the 56-variable HAILFINDER network, with stable performance in all settings.

Missing data imputation remains a fundamental challenge in modern data science, especially when uncertainty quantification is essential. In this work, we propose MissBGM, an AI-powered missing data imputation method via Bayesian generative modeling that bridges the expressive flexibility of neural networks with the statistical rigor of Bayesian inference. Unlike existing methods that often focus on point estimates or treat the missingness mechanism implicitly, MissBGM explicitly and jointly models the data-generating and missingness mechanisms, providing principled posterior uncertainty over imputations rather than a single point estimate. We develop a stochastic optimization framework with alternating updates among missing values, model parameters, and latent variables until convergence. Our theoretical analysis shows that estimates of missing values from MissBGM converge consistently under mild assumptions. Empirically, we demonstrate that MissBGM achieves superior performance over traditional imputers and recent neural network-based methods across extensive experimental settings. These results establish MissBGM as a principled and scalable solution for modern missing data imputation.

Generative models for time-series imputation achieve strong reconstruction accuracy, yet provide no finite-sample reliability guarantees, a critical limitation in power systems where imputed values inform dispatch and planning. We introduce SPLICE (Self-supervised Predictive Latent Inpainting with Conformal Envelopes), a modular framework coupling latent generative imputation with distribution-free, online-adaptive prediction intervals. A JEPA encoder maps daily load segments into a 64-dimensional latent space; a conditional latent bridge with four sampling modes generates candidate gap trajectories; an hourly-conditioned decoder maps back to signal space; and Adaptive Conformal Inference (ACI) wraps the output with coverage-guaranteed prediction bands. The flow-matching variant achieves comparable quality to DDIM in 5--10 ODE steps (5-10x speedup). On thirteen load datasets (nine proprietary, three UCI Electricity, ETTh1), SPLICE achieves the lowest mean Load-only MSE (0.056), winning 9/12 non-degenerate datasets at 91-day gaps and 18/32 across all gap lengths vs. five established baselines, and produces the best CRPS (0.161, -18.3% vs. the strongest competitor). ACI delivers 93--95% empirical coverage, correcting under-coverage failures of up to 7.5 pp observed with static conformal prediction. A pooled JEPA encoder trained on nine feeds transfers to four unseen domains, matching or exceeding per-dataset oracles with only a quick bridge fine-tuning.

Spectral clustering has gained popularity for clustering non-convex data due to its simplicity and effectiveness. It is essential to construct a similarity graph using a high-quality affinity measure that models the local neighborhood relations among the data samples. However, incomplete data can lead to inaccurate affinity measures, resulting in degraded clustering performance. To address these issues, we propose an imputation-free framework with two novel approaches to improve spectral clustering on incomplete data. Firstly, we introduce a new kernel correction method that enhances the quality of the kernel matrix estimated on incomplete data with a theoretical guarantee, benefiting classical spectral clustering on pre-defined kernels. Secondly, we develop a series of affinity learning methods that equip the selfexpressive framework with ℓp-norm to construct an intrinsic affinity matrix with an adaptive extension. Our methods outperform existing data imputation and distance calibration techniques on benchmark datasets, offering a promising solution to spectral clustering on incomplete data in various real-world applications.