In many cases, the widely used matrix inversion approach to describe the spectral interference in collisionally perturbed molecular spectra is not feasible if the particular molecular interactions do not allow the sudden impact approximation (infinitely short collision duration). To overcome this problem, we present a time domain model that describes collisional broadening and narrowing phenomena without requiring the sudden approximation. The key element of the model is a Monte Carlo type sampling process to quantify the temporal autocorrelation of the molecular dipole moment. The spectrum is then obtained numerically via fast Fourier transform. The model does not require a frequency-dependent relaxation operator; the finite collision duration is simply an adjustable parameter in the time domain process. Our approach, which is generally applicable to any set of transition lines, is derived from concepts of both conventional quantum-mechanical and semiclassical theory of line interference. Coherent transfer effects from rotationally inelastic collisions are described as randomly occurring events which affect frequency, amplitude, and phase of the sampled oscillation. Effects of vibrational dephasing are included as well. To demonstrate its feasibility, we apply the model here to the 2.7 mu absorption spectrum of carbon dioxide diluted in high density air (p=43-485 amagat, T=297-754K). The successful modeling of the experimental data, especially the full collapse of P and R branches at ultrahigh densities, accounts for interbranch mixing and for incoherent effects. The calculations make extensive use of the new Hitran (HITEMP) molecular database. Results include revised estimates for the collision duration of CO2 with nitrogen and oxygen at room temperature.