Recent studies on inverse problems have proposed posterior samplers that leverage the pre-trained diffusion models as a powerful prior. The attempts have paved the way for using diffusion models in a wide range of inverse problems. However, the existing methods entail computationally demanding iterative sampling procedures and optimize a separate solution for each measurement, which leads to limited scalability and lack of generalization capability across unseen samples. To address these limitations, we propose a novel approach, Diffusion prior-based Amortized Variational Inference (DAVI) that solves inverse problems with a diffusion prior from an amortized variational inference perspective. Specifically, instead of the separate measurement-wise optimization, our amortized inference learns a function that directly maps measurements to the implicit posterior distributions of corresponding clean data, enabling a single-step posterior sampling even for unseen measurements. The proposed method learns the function by minimizing the Kullback-Leibler divergence between the implicit distributions and the true posterior distributions with multiple measurements using objectives derived based on variational inference. Extensive experiments across three image restoration tasks, e.g., Gaussian deblur, 4x super-resolution, and box inpainting with two benchmark datasets, demonstrate our superior performance over strong diffusion model-based methods.