Inverting corrupted images into the latent space of diffusion models is challenging. Current methods, which encode an image into a single latent vector, struggle to balance structural fidelity with semantic accuracy, leading to reconstructions with semantic drift, such as blurred details or incorrect attributes. To overcome this, we introduce Prompt-Guided Dual Latent Steering (PDLS), a novel, training-free framework built upon Rectified Flow models for their stable inversion paths. PDLS decomposes the inversion process into two complementary streams: a structural path to preserve source integrity and a semantic path guided by a prompt. We formulate this dual guidance as an optimal control problem and derive a closed-form solution via a Linear Quadratic Regulator (LQR). This controller dynamically steers the generative trajectory at each step, preventing semantic drift while ensuring the preservation of fine detail without costly, per-image optimization. Extensive experiments on FFHQ-1K and ImageNet-1K under various inversion tasks, including Gaussian deblurring, motion deblurring, super-resolution and freeform inpainting, demonstrate that PDLS produces reconstructions that are both more faithful to the original image and better aligned with the semantic information than single-latent baselines.
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