Constructing a highly accurate handwritten OCR system requires large amounts of representative training data, which is both time-consuming and expensive to collect. To mitigate the issue, we propose a denoising diffusion probabilistic model (DDPM) to generate training samples. This model conditions on a printed glyph image and creates mappings between printed characters and handwritten images, thus enabling the generation of photo-realistic handwritten samples with diverse styles and unseen text contents. However, the text contents in synthetic images are not always consistent with the glyph conditional images, leading to unreliable labels of synthetic samples. To address this issue, we further propose a progressive data filtering strategy to add those samples with a high confidence of correctness to the training set. Experimental results on IAM benchmark task show that OCR model trained with augmented DDPM-synthesized training samples can achieve about relative word error rate reduction compared with the one trained on real data only.