Expressive Text-to-Speech (TTS) using reference speech has been studied extensively to synthesize natural speech, but there are limitations to obtaining well-represented styles and improving model generalization ability. In this study, we present Diffusion-based EXpressive TTS (DEX-TTS), an acoustic model designed for reference-based speech synthesis with enhanced style representations. Based on a general diffusion TTS framework, DEX-TTS includes encoders and adapters to handle styles extracted from reference speech. Key innovations contain the differentiation of styles into time-invariant and time-variant categories for effective style extraction, as well as the design of encoders and adapters with high generalization ability. In addition, we introduce overlapping patchify and convolution-frequency patch embedding strategies to improve DiT-based diffusion networks for TTS. DEX-TTS yields outstanding performance in terms of objective and subjective evaluation in English multi-speaker and emotional multi-speaker datasets, without relying on pre-training strategies. Lastly, the comparison results for the general TTS on a single-speaker dataset verify the effectiveness of our enhanced diffusion backbone. Demos are available here.