This paper investigates the distributed estimation problem over networks with highly correlated and noisy inputs. As a first step, this paper proposes an algorithm based on diffusion affine projection Versoria (APV) that can process highly correlated input signals over networks. Following that, the optimal step-size is derived by minimizing the mean-square deviation at each node, so that the tradeoff between convergence rate and steady-state error can be addressed. To reduce estimation bias caused by input noise, two diffusion bias-compensated APV (DBCAPV) algorithms are then developed by solving the asymptotic unbiasedness or local constrained optimization problems. Using the optimal step-size processed through the moving average and reset mechanisms, two variable step-size DBCAPV algorithms are obtained. The simulation results demonstrate that our methods are effective.