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Can I run Qwen2-VL-2B on an RTX 5070?

Yes

Its published weights (4.42 GB) fit in the 10.8 GB an RTX 5070 can use, with room for ≈ 32K tokens of context.

Full analysis of Qwen2-VL-2B Everything that runs on RTX 5070 Get the weights on Hugging Face
hf download Qwen/Qwen2-VL-2B

Files and context on RTX 5070

Each file of Qwen2-VL-2B (and of GGUF versions the site has analyzed), and how much context fits next to it, with the context cache in 16-bit or 8-bit.

FileSizeOn RTX 5070 Context (16-bit)Context (8-bit)
As published4.42 GBFits32K32K
4-bit (estimate)1.24 GBFits32K32K

Qwen2-VL-2B on other hardware

Popular models that run on RTX 5070

Assumes 90% of the card's memory is usable and at least 4K tokens of context for one conversation, with the context cache in 16-bit unless noted. Fits leaves at least 20% of that memory for context; Tight leaves less.