A method performed by at least one processing device in an illustrative embodiment comprises applying a first image and a message to an encoder of a steganographic encoder-decoder neural network, generating in the encoder, based at least in part on the first image and the message, a perturbed image containing the message, decoding the perturbed image in a decoder of the steganographic encoder-decoder neural network, and providing information characterizing the decoded perturbed image to the encoder. The generating, decoding and providing are iteratively repeated, with different perturbations being determined in the encoder as a function of respective different instances of the provided information, until the decoded perturbed image meets one or more specified criteria relative to the message. The perturbed image corresponding to the decoded perturbed image that meets the one or more specified criteria relative to the message is output as a steganographic image containing the message.