No, there were not divisions of Koreans that fought with the Soviets

First, the Soviet Union and Japan did not fight during World War II, not until the very end of the war when the USSR entered the war, as discussed at the Yalta Conference in early 1945. I know that's a nit-picky response, but it's an important distinction.

Second, a division is made up of between 10-25,000 personnel. A brigade is 3-5,000 personnel, and a battalion is between 300-1,300 personnel. These numbers depend on country, branch of service, and particular conflict, but these are the ballpark numbers.

The Soviet Union created the 88th Special Independent Sniper Brigade and gave Kim Il-sung command of it in July of 1942 in the Maritime Province (Primorsky Krai). This brigade was made up of only around 600 men from China, Korea, and the Soviet Union. It's mission was one of reconnaissance against the Japanese in Korea and Manchuria. After the war was over, the 88th returned to Korea via Wonsan port under the command of Kim.

The Korean Volunteer Army was an actual division-sized group of Koreans that fought in the Chinese army against the Japanese. After the war, many of them attempted to return to North Korea but were disarmed by the Soviets, who supported Kim and his faction over the Chinese group.

So, to answer your question, there were no divisions of Koreans who fought with the Soviets or Americans to help win their independence from Japan in WW2. There was a Korean division known as the Korean Volunteer Army who fought with the Chinese against the Japanese, and there was a brigade the size of a battalion that the Soviets outfitted and supported for reconnaissance work against the Japanese made up of Koreans, Chinese, and Soviets.

For more information on Kim and his war service, check out Under the Loving Care of the Fatherly Leader by Bradley K. Martin. For information on WW2 and Koreans in general, check out The Korean War: an Encyclopedia by Stanley Sander. The sections on the North Korean military discuss the two factions (Kim and the Soviets vs the Chinese) and their influence on the North Korean military after the war. You can also read The Korean War in History edited by James Cotton and Ian Neary. There are some essays that discuss similar items: North Korean military origins and the Chinese and Soviet influences.