Over the past few years, diffusion models have emerged as novel AI solutions, generating diverse multi-modal outputs from text prompts. Despite their capabilities, they face challenges in computing, such as excessive latency and energy consumption due to their iterative architecture. Although prior works specialized in transformer acceleration can be applied, the iterative nature of diffusion models remains unresolved. In this paper, we present EXION, the first SW-HW co-designed diffusion accelerator that solves the computation challenges by exploiting the unique inter- and intra-iteration output sparsity in diffusion models. To this end, we propose two SW-level optimizations. First, we introduce the FFN-Reuse algorithm that identifies and skips redundant computations in FFN layers across different iterations (inter-iteration sparsity). Second, we use a modified eager prediction method that employs two-step leading-one detection to accurately predict the attention score, skipping unnecessary computations within an iteration (intra-iteration sparsity). We also introduce a novel data compaction mechanism named ConMerge, which can enhance HW utilization by condensing and merging sparse matrices into compact forms. Finally, it has a dedicated HW architecture that supports the above sparsity-inducing algorithms, translating high output sparsity into improved energy efficiency and performance. To verify the feasibility of the EXION, we first demonstrate that it has no impact on accuracy in various types of multi-modal diffusion models. We then instantiate EXION in both server- and edge-level settings and compare its performance against GPUs with similar specifications. Our evaluation shows that EXION achieves dramatic improvements in performance and energy efficiency by 3.2-379.3x and 45.1-3067.6x compared to a server GPU and by 42.6-1090.9x and 196.9-4668.2x compared to an edge GPU.