Latent Video Diffusion Models (LVDMs) have achieved state-of-the-art generative quality for image and video generation; however, they remain brittle under noisy conditioning, where small perturbations in text or multimodal embeddings can cascade over timesteps and cause semantic drift. Existing corruption strategies from image diffusion (Gaussian, Uniform) fail in video settings because static noise disrupts temporal fidelity. In this paper, we propose CAT-LVDM, a corruption-aware training framework with structured, data-aligned noise injection tailored for video diffusion. Our two operators, Batch-Centered Noise Injection (BCNI) and Spectrum-Aware Contextual Noise (SACN), align perturbations with batch semantics or spectral dynamics to preserve coherence. CAT-LVDM yields substantial gains: BCNI reduces FVD by 31.9 percent on WebVid-2M, MSR-VTT, and MSVD, while SACN improves UCF-101 by 12.3 percent, outperforming Gaussian, Uniform, and even large diffusion baselines like DEMO (2.3B) and Lavie (3B) despite training on 5x less data. Ablations confirm the unique value of low-rank, data-aligned noise, and theory establishes why these operators tighten robustness and generalization bounds. CAT-LVDM thus sets a new framework for robust video diffusion, and our experiments show that it can also be extended to autoregressive generation and multimodal video understanding LLMs. Code, models, and samples are available at https://github.com/chikap421/catlvdm

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