We introduce Active Tuning, a novel paradigm for optimizing the internal dynamics of recurrent neural networks (RNNs) on the fly. In contrast to the conventional sequence-to-sequence mapping scheme, Active Tuning decouples the RNN's recurrent neural activities from the input stream, using the unfolding temporal gradient signal to tune the internal dynamics into the data stream. As a consequence, the model output depends only on its internal hidden dynamics and the closed-loop feedback of its own predictions; its hidden state is continuously adapted by means of the temporal gradient resulting from backpropagating the discrepancy between the signal observations and the model outputs through time. In this way, Active Tuning infers the signal actively but indirectly based on the originally learned temporal patterns, fitting the most plausible hidden state sequence into the observations. We demonstrate the effectiveness of Active Tuning on several time series denoising benchmarks, including multiple super-imposed sine waves, a chaotic double pendulum, and spatiotemporal wave dynamics. Active Tuning consistently improves the robustness, accuracy, and generalization abilities of all evaluated models. Moreover, networks trained for signal prediction and denoising can be successfully applied to a much larger range of noise conditions with the help of Active Tuning. Thus, given a capable time series predictor, Active Tuning enhances its online signal filtering, denoising, and reconstruction abilities without the need for additional training.