You've asked a good question but haven't received a good answer. Let's talk a bit about the Soviet atomic program. One of the better books on this subject is David Holloway's Stalin and the Bomb, but I'm sure /u/restricteddata can give you some additional reading as well.
Anyway, even before Operation Barbarossa began in June 1941, the Soviet Union had a moderately robust isotopic enrichment research program. This was mainly blue-sky research, but there were some hopes of eventually harnessing atomic energy.
In 1940 and 1941, according to R. Scott Kemp, the two most favored techniques for isotopic enrichment were thermal diffusion and the gas centrifuge, although other techniques were being pursued as well on a limited basis. The Biogeological Laboratory and the Dnepropetrovsk Physiochemical Institute were some of the leading centers.
The invasion of the Soviet Union almost entirely halted atomic research and research into long-term projects. Pure survival was at stake, which left almost nothing for other causes. Still, in autumn 1941 (and this is incredible to think about when you consider the Germans advancing on Moscow) physicist Georgii Flerov had suspicions that the United States was building an atomic bomb. Independently of the West, he worked out that enriched uranium would be necessary for a fast-fission chain reaction, which he deemed necessary for a bomb.
It wasn't until 1942 that the Soviet Union began a small-scale atomic research program. Stalin was well-informed of American and British atomic research through his spies, but the Soviet atomic scientists were kept in the dark. They didn't know for sure that a bomb could be built until 1943, when Igor Kurchatov, the Oppenheimer of the Soviet program, was allowed to see what had been taken by the spies. He was not allowed to share any of the documents with his fellow scientists.
Even then, Stalin was paranoid that what his spies were sending him was false-flag information, something that would entice the Soviet Union into a costly project it couldn't afford. He hoped Soviet scientists would confirm or deny the research, but he was paranoid of them as well, Holloway writes. He didn't know if they might be pulling the wool over his eyes as well.
Stalin knew of the impending atomic tests by the United States, but not until Hiroshima did he realize the impact of atomic weaponry. "Hiroshima has shaken the whole world," he told Kurchatov. "The balance has been destroyed."
After the war, Stalin would demand that his scientists slavishly copy the American plutonium bomb design, even though they knew there were problems with it and wanted to produce their own design. They got their way with the hydrogen bomb, which was developed largely without espionage assistance.
Now, away from atomics, the Soviet Union made leaps and bounds with conventional military technology during the war. It repeatedly upgraded the T-34 design and unveiled mammoth heavy tanks to complement the medium T-34. In the air, new Soviet aircraft were more than a match for even the improved models of the Bf-109, and Soviet ground support aircraft were stellar when employed properly.