Post-hoc linearization is an attractive way to accelerate pretrained Video Diffusion Transformers (Video DiTs), yet existing methods largely treat the quality loss induced by attention replacement as a recovery problem. We show that a more fundamental bottleneck lies upstream: \emph{initialization}. Random initialization discards pretrained knowledge, whereas manual weight reuse transfers it through rigid and incomplete source--target correspondences. We introduce \textbf{LinMorph}, which recasts Video DiT linearization as a learnable softmax-to-linear weight transformation problem. Instead of copying predefined counterparts, LinMorph learns a cross-parameter morphism that lets each target Gated DeltaNet (GDN) parameter draw jointly from pretrained query, key, value, and output projections, including for parameters with no direct softmax counterpart. A single morphism is shared across layers and learned through local teacher alignment, while producing layer-specific initializations from their respective pretrained weights. The resulting weights are then materialized as independent GDN modules for progressive distillation and joint recovery.Since the morphism operates in weight space rather than token space, it can be learned on short, low-resolution clips and directly reused at larger video scales. Across pretrained Video DiTs, LinMorph enables markedly faster recovery and better final generation quality than random initialization and heuristic weight reuse. Results show that efficient linearization depends not only on how a converted model is recovered, but critically on how pretrained knowledge is transferred before recovery. Project page: https://lonelyling.github.io/LinMorph.

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