Reconstructing dynamic 3D scenes from sparse multi-view videos is highly ill-posed, often leading to geometric collapse, trajectory drift, and floating artifacts. Recent attempts introduce generative priors to hallucinate missing content, yet naive integration frequently causes structural drift and temporal inconsistency due to the mismatch between stochastic 2D generation and deterministic 3D geometry. In this paper, we propose GeoRect4D, a novel unified framework for sparse-view dynamic reconstruction that couples explicit 3D consistency with generative refinement via a closed-loop optimization process. Specifically, GeoRect4D introduces a degradation-aware feedback mechanism that incorporates a robust anchor-based dynamic 3DGS substrate with a single-step diffusion rectifier to hallucinate high-fidelity details. This rectifier utilizes a structural locking mechanism and spatiotemporal coordinated attention, effectively preserving physical plausibility while restoring missing content. Furthermore, we present a progressive optimization strategy that employs stochastic geometric purification to eliminate floaters and generative distillation to infuse texture details into the explicit representation. Extensive experiments demonstrate that GeoRect4D achieves state-of-the-art performance in reconstruction fidelity, perceptual quality, and spatiotemporal consistency across multiple datasets. Project Page: https://mediax-sjtu.github.io/GeoRect4D

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