Structured light, where complex optical fields are tailored in all their degrees of freedom, has become highly topical of late, advanced by a sophisticated toolkit comprising both linear and nonlinear optics. Removing undesired structure from light is far less developed, leveraging mostly on inverting the distortion, e.g., with adaptive optics or the inverse transmission matrix of a complex channel, both requiring that the distortion be fully characterized through appropriate measurement. We show that distortions in spatially structured light can be corrected through difference-frequency generation in a nonlinear crystal without any need for the distortion to be known. We demonstrate the versatility of our approach using a wide range of aberrations and structured light modes, including higher-order orbital angular momentum (OAM) beams, showing excellent recovery of the original undistorted field. To highlight the efficacy of this process, we deploy the system in a prepare-and-measure communications link with OAM, showing minimal cross talk even when the transmission channel is highly aberrated, and outline how the approach could be extended to alternative experimental modalities and nonlinear processes. Our demonstration of light-correcting light without the need for measurement opens an approach to measurement-free error correction for classical and quantum structured light, with direct applications in imaging, sensing, and communication.