Variation of Arctic sea ice has significant impacts on polar ecosystems, transporting routes, coastal communities, and global climate. Tracing the change of sea ice at a finer scale is paramount for both operational applications and scientific studies. Recent pan-Arctic sea ice forecasting methods that leverage advances in artificial intelligence has made promising progress over numerical models. However, forecasting sea ice at higher resolutions is still under-explored. To bridge the gap, we propose a two-staged deep learning framework, IceDiff, to forecast sea ice concentration at finer scales. IceDiff first leverages an independently trained vision transformer to generate coarse yet superior forecasting over previous methods at a regular 25km x 25km grid. This high-quality sea ice forecasting can be utilized as reliable guidance for the next stage. Subsequently, an unconditional diffusion model pre-trained on sea ice concentration maps is utilized for sampling down-scaled sea ice forecasting via a zero-shot guided sampling strategy and a patch-based method. For the first time, IceDiff demonstrates sea ice forecasting with the 6.25km x 6.25km resolution. IceDiff extends the boundary of existing sea ice forecasting models and more importantly, its capability to generate high-resolution sea ice concentration data is vital for pragmatic usages and research.