We develop DEEPTRAVERSAL, a feedback-driven framework to test DNNs. DEEPTRAVERSAL first launches an offline phase to map media data of various forms to manifolds. Then, in its online testing phase, DEEPTRAVERSAL traverses the prepared manifold space to maximize DNN coverage criteria and trigger prediction errors. In our evaluation, DNNs executing various tasks (e.g., classification, self-driving, machine translation) and media data of different types (image, audio, text) were used. DEEPTRAVERSAL exhibits better performance than prior methods with respect to popular DNN coverage criteria and it can discover a larger number and higher quality of error-triggering inputs. The tested DNN models, after being repaired with findings of DEEPTRAVERSAL, achieve better accuracy