Molecular multiple-input-multiple-output (MIMO) techniques are proposed in the literature to improve the overall throughput of molecular communication via diffusion (MCvD) systems. Among these methods, molecular index modulation (molecular-IM) schemes are recently introduced as novel molecular MIMO approaches to provide significant improvements in terms of communication efficiency. However, despite molecular-IM's strong combating capability against inter-symbol interference (ISI) and inter-link interference (ILI), they are still prone to them due to the characteristics of a molecular MIMO MCvD channel. With the goal of further mitigating ISI and ILI, this letter introduces memory-assisted, linear time and space-time equalization methods for molecular-IM schemes. It is shown that the proposed equalization methods yield significant improvements in error performance while retaining low decoding complexity due to the linear combining.