We present a diffusion-based image morphing approach with perceptually-uniform sampling (IMPUS) that produces smooth, direct, and realistic interpolations given an image pair. A latent diffusion model has distinct conditional distributions and data embeddings for each of the two images, especially when they are from different classes. To bridge this gap, we interpolate in the locally linear and continuous text embedding space and Gaussian latent space. We first optimize the endpoint text embeddings and then map the images to the latent space using a probability flow ODE. Unlike existing work that takes an indirect morphing path, we show that the model adaptation yields a direct path and suppresses ghosting artifacts in the interpolated images. To achieve this, we propose an adaptive bottleneck constraint based on a novel relative perceptual path diversity score that automatically controls the bottleneck size and balances the diversity along the path with its directness. We also propose a perceptually-uniform sampling technique that enables visually smooth changes between the interpolated images. Extensive experiments validate that our IMPUS can achieve smooth, direct, and realistic image morphing and be applied to other image generation tasks.