We start from the simplest case with one transmit antenna and multiple receive antenna. This is also called single-input-multiple-output (SIMO).
The signal model can be written as
\[y_\ell[m] = h_\ell[m] x[m] + w_\ell[m] \qquad \ell=1,\ldots,L,\]where $L$ is the number of receive antennas, $m$ is the index of the time slot, $h_\ell[m]$ is the channel gain from the transmit antenna to the $\ell$-th receive antenna, $x[m]$ is the transmit signal, $w_\ell[m] \sim \mathcal{CN}(0,N_0)$ is the additive Gaussian noise, and $y_\ell[m]$ is the receive signal at the $\ell$-th receive antenna.
In this case, we essentially send multiple copies of the transmit signal to the receive antennas. The signal model is fundamentally the same as that in repetition coding.
Therefore, assuming that the channel gains to different receive antennas are independent, we can achieve the same diversity gain of $L$ as in time diversity. Such a diversity gain can be realized by either coherent or noncoherent detection.