The recommended months for confirmed liveaboard departures are from November to May but the Maldives scuba diving holiday season runs all year round. If you wish to come outside of November to May it may be more difficult to find a departure date that suits you.
The northeast monsoon (winds from the northeast) runs from the end of December to May. At this time of year the skies are blue and the lack of wind means the seas are calm. The visibility on the eastern side of the atolls is good at 20-30+m, and 15-20m on the western sides. The eastern atolls generally have the best visibility during this time too, and December to March normally enjoys the best overall visibility. This is because the currents flow through the atoll channels from east to west. Reef sharks gather in large numbers at the channel entrances on the eastern side of the atolls; whereas mantas are drawn to the western sides because plankton flows out of the channels into open sea on west at this time. The current is strongest at this time of year too.
June to November is the southwest monsoon and the above process is reversed: currents from through the channels in an easterly direction; mantas to the east, reef sharks and better visibility to the west. It is at this time when the skies are cloudier, the winds are stronger and seas a little rougher, although the season does still get nice, sunny spells. Surface swells can reach 1-2m, particularly during the rainy season in June/July, when rain falls on average 3-4 hours per day, and during the monsoon transitions in late May and early December.
Water temperature are fairly constant throughout the year at 26-29°C, except in the far south where the water temperature can drop to 24°C during the northeast monsoon.
Having said all that, like most places in the world, the seasons in the Maldives have become less predictable in recent years.
Mantas, whale sharks, turtles, reef sharks and hammerhead sharks are found in the Maldives all year round; if anything, manta rays are found in even greater numbers in the southwest monsoon. As for the other big creatures, diver encounters are dependent on non-seasonal factors: whale sharks are more frequently sighted at high tide, and hammerhead sharks ascend to shallower water at sunrise.
The exception to this is at Hanifaru Bay, usually between August and November, when hundreds of manta rays and some whale sharks gather on the eastern side of Baa, where vast plankton fields accumulate. The area has been declared a marine reserve and current regulations permit snorkeling only for a maximum of 60 persons at a time.