In this paper, we further develop our framework to design new assistance and rehabilitation protocols based on motor primitives. In particular, we extend our recent results of oscillator-based assistance to the case of walking. The adaptive oscillator used in this paper is capable of predicting the angular position of the user's joints in the future, based on the pattern learned during preceding cycles. Assistance is then provided by attracting the joints to this future position using a force field in a compliant lower-limb exoskeleton. To demonstrate the method efficiency, we computed the rate of metabolic energy expended by the participants during a walking task, with and without assistance. Results show a significant decrease of energy expenditure with the assistance switched on, although not to a point to entirely compensate for the burden due to the exoskeleton lack of transparency. The results further show changes in the kinematics: with assistance, the participants walked with a faster cadence and ampler movements. These results tend to prove the relevance of designing assistance protocols based on adaptive oscillators (or primitives in general) and pave the way to the design of new rehabilitation protocols.