Multimodal Emotion Recognition in Conversation (MERC) requires sophisticated reasoning over heterogeneous data streams. A significant challenge arises from modality corruption, encompassing missing data points, low signal-to-noise ratios, and ambiguous cues that obscure true emotional states. Existing approaches often rely on static fusion strategies whose predefined, data quality-agnostic operations leave them incapable of data imputation and noise suppression. To address this gap, we propose Latent Conversational Data Repair (L-CoDeR), a novel framework that dynamically performs distribution-preserving data imputation in a learned latent space for emotion recognition. In our L-CoDeR framework, we design three core components: the context-guided latent diffusion model to perform high-fidelity imputation that is coherent with conversational dynamics, the Distribution-Preserving Overlay module to purify repaired features and prevent distributional drift via affine calibration and similarity-gating, and the structure-aware Graph Neural Networks (GNNs) to perceive the conversational structure for robust final classification. On the challenging IEMOCAP and MELD benchmarks, L-CoDeR establishes new state-of-the-art (SOTA) results for both Accuracy (Acc) and Weighted Average F1-score (WA-F1). Its demonstrated effectiveness in repairing corrupted, real-world conversational data highlights its strong potential for socially-aware applications.