Near the end of the Second World War, the Soviet Union began to invade Japanese holdings in Manchuria and Korea, greatly pressuring the Imperial government and military. This, combined with the threat of the atomic bombs, forced Japan to capitulate and be occupied by the US postwar, reforming into what it is today.
It is my general understanding that many believe that were the bombs not used and Operation Downfall launched, the Soviets would have fully invaded the Korean Peninsula and the northern Japanese mainland, resulting in a North-South division of the country by the rising factions of the coming Cold War.
The Soviets would have completely taken Korea in this scenario, that much is certain, however I do not know how they could have threatened the mainland. From what I know, the Soviet military was comprised mainly of the Red Army, with the Air Force being secondary and the Navy an afterthought. Therefore, their Navy was rather small by comparison to their contemporaries at the time.
Looking over plans for Operation Downfall, the only reason why I see it could have been done was through the monstrous amount of amphibious assault ships and troops built up as a result of the “island hopping” campaign. Since the Soviets never performed such operations, they logically would therefore not have such a capability.
With this in mind, how could the Soviets invade mainland Japan given their severe lack of amphibious forces?
The Soviets did do some amphibious landings towards the end of the war, taking the Kuril Islands in late August and September 1945. They did so by launching off of Sakhalin and Kamchatka.
Similarly, their plan for invading Japan was to invade Hokkaido through Sakhalin. /u/The_Alaska discusses this in some detail in this thread from a few years ago, while /u/Acritas reproduces the Soviet battle plans here.
You have to keep in mind that attacking from the north was a very different sort of thing from attacking from the south/east as the United States was doing, and also that even though the Soviet experience at this sort of thing was low, they did have quite a lot of troops at their disposal and the Japanese were at that point stretched pretty thin. It was a credible threat. Would they have suffered heavy losses from it? Quite possibly, but that was not the sort of thing that would put Stalin off, which is exactly why the Japanese military analysts feared it so much (they believed that heavy losses against the United States might drive them to negotiation, but had no such illusions about Stalin).
One could ask: if attacking from the north was so much easier, why didn't the US do it? Because that would require moving troops and supply lines all the way through the Soviet Union, which was neither an option (Stalin wasn't going to let another army, even an allied one, occupy his territory) nor particularly feasible (the logistics of even trying to move troops into China proved exceedingly difficult for the Allies).