The restoration of nonuniform distorted infrared (IR) images is crucial for human visual perception and subsequent application tasks. However, existing methods sometimes fail to yield visually natural decompositions and perform insufficiently in the preservation of meaningful structures while suppressing disturbing noise. A spatially adaptive hybrid ℓ₁  −  ℓ₂ variational framework for the nonuniform intensity correction of IR images is proposed. Considering the piecewise constant characteristics of latent images, a weighted ℓ₁-norm regularization method is developed to constrain the local affinity of neighborhood pixels according to their intensity and structural priors, thereby significantly preserving structures while smoothly flattening areas. Additionally, an ℓ₂-norm guided local smoothness constraint is incorporated with an absolute scale term provided by coarse estimation to characterize the bias field component to restrict potential solutions and enforce the bias component to be textureless. Moreover, the proposed ℓ₁  −  ℓ₂ model is efficiently solved by an alternating direction method of multipliers scheme. Extensive experiments on both synthesized images and two real-world IR datasets indicate that the performance of the proposed method is superior to that of five existing algorithms both visually and numerically.