Generative Feature Imputing

• Generative feature imputing is a modeling paradigm that reconstructs missing data by sampling from conditional generative priors using observed data and missingness masks.
• It encompasses diverse methodologies including adversarial, VAE, diffusion, and sequential refining approaches to handle different types of data and missingness patterns.
• The framework addresses challenges under MCAR, MAR, and MNAR mechanisms, employing tailored loss functions and architectures to ensure plausible and accurate imputations.

Searching arXiv for papers on generative feature imputation and closely related generative imputation methods. Generative feature imputing denotes a family of methods that reconstruct missing, corrupted, or erased features by sampling from a learned generative prior conditioned on the available observations and an explicit missingness mask. In the most specific usage represented by recent semantic communication work, it is a receiver-side mechanism that takes as input a quantized feature tensor $$\hat{\mathbf y}\in\mathcal U^{W_y\times H_y\times C_y}$$ with erasures, identifies the erased spatial support through a binary mask $\mathbf M\in\{0,1\}^{W_y\times H_y}$, and reconstructs the missing feature entries with a diffusion-model-based generator (Huang et al., 25 Aug 2025). More broadly, the same term aligns with a larger literature on generative imputation for tabular, multimodal, tensor, and image data, where the common objective is to learn conditional distributions such as $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$ or $p(x_u\mid x_o)$ and use them to produce plausible completions under MCAR, MAR, or MNAR missingness (Mahmud et al., 5 Dec 2025, Ma et al., 2021).

1. Conceptual scope and problem formulation

Generative feature imputing addresses incomplete data by treating missing values not merely as nuisance variables to be filled with point estimates, but as latent quantities to be inferred from a learned conditional generative model. A standard formulation introduces a data vector $x$, a binary mask $M\in\{0,1\}^d$ indicating observed and missing entries, and a decomposition into $x_{\mathrm{obs}}=M\odot x$ and $x_{\mathrm{mis}}=(1-M)\odot x$. The target is then to learn $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$ so that plausible completions can be sampled for arbitrary missingness patterns (Mahmud et al., 5 Dec 2025). Closely related notation appears in MNAR modeling, where $X=(X_1,\dots,X_D)$, $\mathbf M\in\{0,1\}^{W_y\times H_y}$0, $\mathbf M\in\{0,1\}^{W_y\times H_y}$1 denotes observed features, $\mathbf M\in\{0,1\}^{W_y\times H_y}$2 missing features, and $\mathbf M\in\{0,1\}^{W_y\times H_y}$3 latent variables that may encode unobserved confounders (Ma et al., 2021).

The field spans several distinct regimes. In semantic communication, the missing object is not a conventional tabular feature vector but a transmitted latent feature tensor whose entries may be erased by packet loss. The receiver observes a corrupted tensor $\mathbf M\in\{0,1\}^{W_y\times H_y}$4, constructs a mask $\mathbf M\in\{0,1\}^{W_y\times H_y}$5, and invokes a learned feature-space prior to restore the lost entries (Huang et al., 25 Aug 2025). In multimodal diagnosis, missingness appears at the modality level, for example when T1-weighted MRI or functional network connectivity is absent for a subject, and the generator maps from the available modality to the missing one (Hassanzadeh et al., 12 Aug 2025). In sparse educational data, the incomplete object is a three-dimensional learner–question–attempt tensor $\mathbf M\in\{0,1\}^{W_y\times H_y}$6, with missing entries corresponding to unattempted questions (Zhang et al., 2024). In image inpainting, feature imputation may occur internally within convolutional layers, where missing feature responses are replaced by learned local estimates rather than treated as ordinary inputs (Hukkelås et al., 2020).

A major axis of variation is the missingness mechanism. Some methods are developed and evaluated under MCAR, where entries are removed uniformly at random (Camino et al., 2019, Kachuee et al., 2019). Others explicitly address MAR, including blockwise multiple imputation with conditional WGANs (Dai et al., 2021). A further line targets MNAR, where the cause of missingness is not fully observed and the missingness mechanism itself must be modeled or jointly reconstructed (Chen et al., 2023, Ma et al., 2021). This suggests that “generative feature imputing” is best understood as a modeling paradigm rather than a single architecture: it combines conditional generation, masking, and an explicit representation of uncertainty over unobserved features.

2. Core model families

A large portion of the literature uses adversarial learning. In ImpuGAN, a conditional GAN is trained on complete samples so that the generator reconstructs missing entries from available features and the discriminator distinguishes true from imputed data. The generator receives $\mathbf M\in\{0,1\}^{W_y\times H_y}$7, $\mathbf M\in\{0,1\}^{W_y\times H_y}$8, and $\mathbf M\in\{0,1\}^{W_y\times H_y}$9, outputs a candidate $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$0, and the final imputed sample is $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$1 (Mahmud et al., 5 Dec 2025). GAIN-style formulations follow the same basic template, with the discriminator predicting which entries were observed and the generator attempting to fool it while respecting observed coordinates (Camino et al., 2019, Friedjungová et al., 2020). Wasserstein variants replace the standard adversarial criterion with an Earth-Mover objective and a critic constrained to be 1-Lipschitz, as in WGAIN (Friedjungová et al., 2020). Feature-specific formulations such as IFGAN split the problem across columns, using a separate generator–discriminator pair for each feature so that each $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$2 models $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$3 conditioned on $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$4 (Qiu et al., 2020). Class-conditional adversarial imputers such as CGAIN further concatenate one-hot labels into the generator and discriminator to learn class-specific distributions under imbalance (Awan et al., 2020).

Variational and latent-variable models constitute a second major family. VAE-based imputers train encoder–decoder models on incomplete inputs, typically penalizing reconstruction only on observed dimensions and imputing the missing entries from $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$5 and $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$6 (Camino et al., 2019). Under MNAR, identifiable latent-variable formulations become central. GINA factors the joint density as $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$7, combines an identifiable VAE-style reference model with a missingness network $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$8, and uses an importance-weighted variational bound for training (Ma et al., 2021). The GNR model instead treats complete data and the missing mask as “two modalities of incomplete data on an equal footing,” introduces a “conjunction model” decomposition to represent their distributions in parallel, and concurrently imputes incomplete data and reconstructs the missing mask in latent space (Chen et al., 2023).

Diffusion-based models represent a newer direction. In the semantic communication framework, a latent diffusion model $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$9 with a UNet backbone is conditioned on the corrupted feature tensor $p(x_u\mid x_o)$0 and the error mask $p(x_u\mid x_o)$1. The forward process noises a clean feature tensor $p(x_u\mid x_o)$2 via

$p(x_u\mid x_o)$3

and the reverse DDIM sampler reconstructs the clean features over $p(x_u\mid x_o)$4 denoising steps (Huang et al., 25 Aug 2025). The training loss is a masked noise-prediction objective. The paper states that the diffusion UNet is trained to predict the added noise only on erased positions via

$p(x_u\mid x_o)$5

(Huang et al., 25 Aug 2025).

A fourth family uses sequential refinement. “Data Generation as Sequential Decision Making” formulates imputation as a finite-horizon MDP in which an agent iteratively updates a running guess $p(x_u\mid x_o)$6 for the missing coordinates and is trained through guided policy search (Bachman et al., 2015). The final prediction is decoded from $p(x_u\mid x_o)$7, and the cost is the negative log-likelihood of the unknown coordinates under the terminal prediction. This line differs from one-shot conditional generation by making imputation explicitly iterative and policy-driven.

3. Conditioning, masking, and feature-space representations

The mask is not merely a bookkeeping device; it is an active conditioning variable and, in several models, an object of reconstruction in its own right. In tabular cGAN imputation, the generator is typically conditioned on $p(x_u\mid x_o)$8, $p(x_u\mid x_o)$9, and noise, while the discriminator is given a completed sample together with the mask or a hint vector derived from it (Mahmud et al., 5 Dec 2025, Friedjungová et al., 2020). The hint mechanism is central in GAIN-style models because it partially reveals the true mask to the discriminator, preventing trivial solutions and accelerating convergence (Friedjungová et al., 2020, Awan et al., 2020). In the categorical EHR setting, both generator and discriminator operate on recoded categorical feature blocks, and the discriminator predicts whether each feature block was originally observed (Yang et al., 2021).

Handling heterogeneous feature types requires architectural modification. ImpuGAN states that continuous features are output directly, whereas categorical columns use mode-specific normalization and a hard-sampling “logit override” to produce one-hot vectors (Mahmud et al., 5 Dec 2025). It also introduces a multi-condition mechanism: for any subset of observed categorical attributes $x$0, a multi-hot conditioning vector is formed and fed into both generator and discriminator so that imputations respect user-specified conditions (Mahmud et al., 5 Dec 2025). Earlier VAE- and GAN-based comparative work addressed mixed data through “variable splitting,” in which the final layer is divided into per-variable heads, with sigmoid activations for numeric variables and Gumbel-Softmax for categorical variables, while categorical inputs may be embedded before concatenation with numeric ones (Camino et al., 2019). Categorical GAIN stabilizes adversarial training by “fuzzy binary coding,” which maps hard one-hot or multi-label binaries into $x$1 so that the discriminator cannot exploit a trivial domain mismatch between real $x$2 codes and soft generator outputs (Yang et al., 2021).

Feature-space imputation is especially explicit in semantic communication. The framework begins from a quantized feature tensor $x$3 partitioned into nonoverlapping patches of size $x$4. Each patch is serialized into a packet, and packet failures erase all $x$5 spatial locations across every channel, thereby concentrating corruption into contiguous feature-space blocks (Huang et al., 25 Aug 2025). The receiver constructs a preliminary binary indicator $x$6, dilates it with a $x$7 all-ones kernel $x$8, and obtains a spatial mask $x$9 marking the regions to be regenerated (Huang et al., 25 Aug 2025). This is a distinctive use of masking: the mask is engineered through packetization and morphological expansion so that the generative model solves a structured inpainting problem in latent feature space rather than a scattered reconstruction problem.

Some architectures impute features internally, layer by layer. Image inpainting with learnable feature imputation introduces an “Imputed Convolution” in which each uncertain feature $M\in\{0,1\}^d$0 is replaced by the expectation of a random variable $M\in\{0,1\}^d$1 that equals the original value with probability $M\in\{0,1\}^d$2 and an imputed value $M\in\{0,1\}^d$3 otherwise. The expectation is

$M\in\{0,1\}^d$4

and $M\in\{0,1\}^d$5 is defined as a learned, certainty-weighted neighborhood average (Hukkelås et al., 2020). The certainty map is also propagated through the network. This mechanism treats feature imputation as an internal primitive of convolution, not only as a preprocessing step.

4. Missingness mechanisms and identifiability

The literature distinguishes sharply between MCAR, MAR, and MNAR, because generative imputation quality depends not only on model capacity but also on whether the missingness process is represented correctly. Much early comparative work evaluates under MCAR, where values are randomly removed and models are judged by RMSE or downstream accuracy after reconstruction (Camino et al., 2019, Kachuee et al., 2019). Such settings are methodologically convenient but do not capture the bias induced by informative missingness.

For MAR, MI-GAN develops a multiple imputation method for high-dimensional blockwise missing value problems. The data are partitioned into missingness patterns $M\in\{0,1\}^d$6, with pattern-specific masks $M\in\{0,1\}^d$7, and for each incomplete pattern a conditional WGAN learns $M\in\{0,1\}^d$8 from complete cases (Dai et al., 2021). The generator forms a noisy partial vector $M\in\{0,1\}^d$9, the discriminator acts as a critic with gradient penalty, and multiple imputations are produced by repeated sampling of $x_{\mathrm{obs}}=M\odot x$0, after which Rubin’s combining rules are used for inference (Dai et al., 2021). The stated motivation is not only imputation error but also valid statistical inference under MAR.

MNAR poses a stricter challenge because the missingness may depend on the unseen values themselves. GINA explicitly studies the identifiability of generative models under MNAR. Its central factorization is the selection model

$x_{\mathrm{obs}}=M\odot x$1

with a latent-confounder extension in which both $x_{\mathrm{obs}}=M\odot x$2 and $x_{\mathrm{obs}}=M\odot x$3 depend on $x_{\mathrm{obs}}=M\odot x$4 (Ma et al., 2021). The paper states an informal proposition: under assumptions including model-family correctness, “subset identifiability,” and positivity of observation patterns, the maximum-likelihood solution yields a unique reference parameter $x_{\mathrm{obs}}=M\odot x$5, though $x_{\mathrm{obs}}=M\odot x$6 may remain non-unique (Ma et al., 2021). This is an important correction to the common practice of applying deep generative models to MNAR without analyzing whether their parameters are recoverable.

The GNR paper also targets MNAR, but it criticizes a different aspect of existing methods. It states that directly incorporating statistical MNAR decompositions into deep generative models is sub-optimal because they neglect the confidence of the reconstructed mask during imputation, leading to insufficient information extraction and less-guaranteed imputation quality (Chen et al., 2023). Its proposed remedy is to regard the complete data and missing mask as two modalities, represent them in parallel with a conjunction-model decomposition, and jointly impute data while reconstructing the missing mask (Chen et al., 2023). This suggests a conceptual shift from modeling the mask solely as an auxiliary variable toward treating it as a co-equal information source.

A recurrent misconception is that strong generative performance under MCAR automatically transfers to MNAR. The available evidence does not support that generalization. Several papers explicitly limit experiments to MCAR or MAR (Camino et al., 2019, Kachuee et al., 2019, Dai et al., 2021), while the MNAR-focused papers emphasize the need to model missingness or establish identifiability (Ma et al., 2021, Chen et al., 2023). A plausible implication is that “generative feature imputing” is not a single statistical assumption but a framework whose validity depends on whether the conditioning set includes the relevant missingness information.

5. Domain-specific realizations

The semantic communication formulation is unusually explicit about system-level design. The framework comprises three key techniques: spatial error concentration packetization, diffusion-based generative feature imputing, and semantic-aware power allocation (Huang et al., 25 Aug 2025). The packetization strategy maps each latent feature patch $x_{\mathrm{obs}}=M\odot x$7 to a packet $x_{\mathrm{obs}}=M\odot x$8, so a single packet failure erases a small contiguous spatial block across all channels (Huang et al., 25 Aug 2025). The diffusion imputer then reconstructs the erased features conditioned on the corrupted tensor and the dilated mask. Finally, semantic-aware power allocation uses a Class Activation Map derived from a pretrained classification backbone to assign larger power to semantically important packets via an optimization problem over per-packet powers $x_{\mathrm{obs}}=M\odot x$9 (Huang et al., 25 Aug 2025). Under AWGN and i.i.d. block Rayleigh fading, the paper reports higher semantic accuracy and lower LPIPS than DJSCC and JPEG2000, as well as substantial gains under packet erasure (Huang et al., 25 Aug 2025).

In multimodal Alzheimer’s disease diagnosis, the missing object is an entire modality. The proposed model uses two generators, $x_{\mathrm{mis}}=(1-M)\odot x$0 and $x_{\mathrm{mis}}=(1-M)\odot x$1, together with corresponding discriminators $x_{\mathrm{mis}}=(1-M)\odot x$2 and $x_{\mathrm{mis}}=(1-M)\odot x$3, trained with least-squares adversarial losses, cycle consistency, and an identity loss over paired subjects (Hassanzadeh et al., 12 Aug 2025). The dataset consists of 986 subjects and 2923 total scans from ADNI, with severe modality imbalance between T1 and FNC (Hassanzadeh et al., 12 Aug 2025). At inference time, the available modality is used to synthesize the missing one, and the completed subject representation is passed to a multimodal classifier. The reported classification accuracy for AD versus CN is $x_{\mathrm{mis}}=(1-M)\odot x$4, compared with $x_{\mathrm{mis}}=(1-M)\odot x$5 for subsampling and $x_{\mathrm{mis}}=(1-M)\odot x$6 for zero-imputation, with relative improvements of $x_{\mathrm{mis}}=(1-M)\odot x$7 and $x_{\mathrm{mis}}=(1-M)\odot x$8 respectively (Hassanzadeh et al., 12 Aug 2025). The paper interprets this as disease-pattern preservation through cycle consistency and identity anchoring.

Educational data introduce higher-order sparsity. The customized 3D GAIN method represents responses as a tensor $x_{\mathrm{mis}}=(1-M)\odot x$9, where $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$0 is 1 for a correct response, 0 for incorrect, and missing if the learner never attempted the question at that attempt index (Zhang et al., 2024). The generator and discriminator are implemented with convolutional stacks over each learner slice $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$1, and optimization uses a least-squares GAN loss plus a reconstruction term on observed entries (Zhang et al., 2024). On six Intelligent Tutoring System datasets, the method reportedly achieves 5–15% lower RMSE than CPD, BPTF, standard GAN, and InfoGAN baselines, especially when sparsity exceeds 70% (Zhang et al., 2024). Here generative feature imputing is closely tied to preserving multi-way structure.

Image inpainting forms another branch. In “Image Inpainting with Learnable Feature Imputation,” the central innovation is not direct synthesis of pixels but a convolutional primitive that imputes uncertain feature values before convolution, propagates non-binary certainty, and is used inside a U-Net trained only with adversarial loss and a revised gradient penalty (Hukkelås et al., 2020). On the FDF dataset, the ablation table reports that adding the revised gradient penalty improves FID from 6.15 to 1.83, and the final configuration with IConv and MSG-GAN reaches LPIPS 0.0728, PSNR 24.01, and FID 1.49 (Hukkelås et al., 2020). This suggests that generative feature imputing can operate at intermediate feature layers rather than only on end-level missing variables.

Blockwise matrix completion highlights the role of long-range dependencies. BlockEcho pretrains a matrix factorization $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$2, uses the resulting embeddings $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$3 to guide a GAN generator, and adds a second discriminator $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$4 that compares the generator’s intermediate embeddings with the pretrained MF embeddings (Han et al., 2024). On public datasets across traffic flow, COVID-19, and MovieLens, the paper states that BlockEcho achieves the lowest RMSE on all five datasets under block-wise masking at 60% missing, and that its advantage grows at high missing rates (Han et al., 2024). This domain illustrates that feature imputation may need explicitly global structure when local neighborhoods are uninformative.

6. Training objectives, evaluation criteria, and empirical patterns

Despite architectural diversity, several objective patterns recur. Adversarial losses are usually combined with a fidelity or reconstruction term. ImpuGAN defines

$p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$5

and an optional reconstruction loss

$p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$6

combined in a minimax objective with a reconstruction weight $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$7 (Mahmud et al., 5 Dec 2025). GAIN-style models similarly combine an adversarial term with reconstruction on observed entries (Camino et al., 2019, Friedjungová et al., 2020). Cycle-consistent multimodal translation adds cycle and identity losses (Hassanzadeh et al., 12 Aug 2025). MNAR latent-variable methods instead optimize likelihood surrogates such as MIWAE-style importance-weighted bounds (Ma et al., 2021). Diffusion-based methods optimize masked denoising objectives (Huang et al., 25 Aug 2025).

The following table summarizes representative formulations drawn directly from the cited papers.

Setting	Generative mechanism	Representative objective
Tabular conditional imputation	cGAN	$p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$8 (Mahmud et al., 5 Dec 2025)
MNAR latent-variable imputation	identifiable generative model	MIWAE-style importance-weighted bound $p(x_{\mathrm{mis}}\mid x_{\mathrm{obs}},M)$9 (Ma et al., 2021)
Semantic communication	latent diffusion	masked diffusion loss $X=(X_1,\dots,X_D)$0 on erased positions [2508