Denoising diffusion models represent a recent emerging topic in computer vision, demonstrating remarkable generative results. These models are widely appreciated for the quality and diversity of the generated samples, but they suffer from a very high computational overhead due to the large number of steps (passes through the network) involved during sampling. To this end, we propose to develop more efficient diffusion models via curriculum learning, a strategy to train neural networks from easy to hard. We will consider multiple curriculum learning strategies, revolving around novel model-level and data-level curriculum methods adapted for diffusion models, such as gradually reducing the size of the input (along with the size of the neural model) as the noise level increases (since the level of information to be learned decreases), or training the model on samples with increasingly lower noise levels, considering that the level of noise is inversely proportional to the difficulty of the samples. Aside from considering such curriculum learning strategies as alternative options, we aim to jointly combine them in unified curriculum learning strategies, to jointly benefit from the advantages brought by each strategy.