We present a diffusion-based bias-compensated recursive least squares (RLS) algorithm for distributed estimation in ad-hoc adaptive sensor networks where nodes cooperate to estimate a common deterministic parameter vector. It is assumed that both the regressors and the output response are corrupted by stationary additive noise. In this case, the least-squares estimator is biased. Assuming that a good estimate of the noise statistics is available, this bias can be removed at the cost of a larger variance of the estimator. However, by letting nodes cooperate in a diffusion-based fashion, it is possible to significantly reduce the variance, and furthermore improve the stability of the algorithm. If there are estimation errors in the noise statistics, the diffusion also results in a smaller residual bias. We provide closed-form expressions for the residual bias and mean-square deviation of the estimate (without full derivations). We also provide simulation results to demonstrate the beneficial effect of diffusion.