State-of-the-art base stations can be equipped with a massively large number of antenna elements, often several hundreds of elements, thanks to the rapid advancement of wideband radio-frequency (RF) analog circuits and compact antenna design techniques. With massive antenna systems, a relatively large number of users can be served at the same time by means of analog and digital beamforming and spatial multiplexing. We investigate such a large-scale multi-user multipleinput multiple-output (MU-MIMO) wireless system employing an orthogonal frequency-division multiplexing (OFDM)-based downlink transmission scheme. The use of OFDM causes a high peak-to-average power ratio (PAPR), which usually calls for expensive and power-inefficient RF components at the base station. In this paper, we propose a nullspace vector perturbation (VP) which integrates both nonlinear lattice and linear subspace precoding approaches. By exploiting high degrees of freedom available in massive MU-MIMO OFDM systems, the signal PAPR can be significantly reduced with the proposed method. We also introduce a Gaussian process (GP) regression approach to be robust against the imperfect channel knowledge, which is required for the VP operation, in time-varying fading channels. Our analysis of outage capacity reveals that the proposed VP with GP regression offers a significant improvement in sum-rate spectral efficiency while reducing the PAPR.