Backbone training-free video editing built on pre-trained text-to-image (T2I) diffusion models enables lightweight, prompt-driven edits without additional finetuning. A critical yet often overlooked factor is cross-frame latent selection during DDIM inversion, which largely determines spatiotemporal coherence in the subsequent denoising process. Existing pipelines typically rely on static, heuristic keyframe policies and temperature-softmax responsibilities, yielding unscalability i.e., numerical sensitivity and scale bias, that degrades generalization across diverse scenes. In this paper, we propose VIVID (Variational Inference for Video editing with Image Diffusion), an uncertainty-aware variational latent anchoring module that dynamically selects informative frames and compresses cross-frame latents into a compact set of semantic anchors. VIVID learns stable assignments via a variational objective with contrastive alignment and prior regularization, producing anchors that preserve spatial details while enforcing temporal continuity, and can be plugged into existing backbone training-free T2I-based video editing frameworks as a drop-in replacement for heuristic selection. Extensive experiments on standard benchmarks and in-the-wild videos demonstrate that VIVID achieves state-of-the-art inversion fidelity, editing quality, and temporal consistency, while reducing memory and runtime compared with prior backbone training-freebaselines. Code is released in: https://github.com/amasawa/VIVID.
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