Distributed training is essential for scaling the training of large neural network models, such as large language models (LLMs), across thousands of GPUs. However, the complexity of distributed training programs makes them particularly prone to silent bugs, which do not produce explicit error signal but lead to incorrect training outcome. Effectively detecting and localizing such silent bugs in distributed training is challenging. Common debugging practice using metrics like training loss or gradient norm curves can be inefficient and ineffective. Additionally, obtaining intermediate tensor values and determining whether they are correct during silent bug localization is difficult, particularly in the context of low-precision training. To address those challenges, we design and implement TTrace, the first system capable of detecting and localizing silent bugs in distributed training. TTrace collects intermediate tensors from distributing training in a fine-grained manner and compares them against those from a trusted single-device reference implementation. To properly compare the floating-point values in the tensors, we propose novel mathematical analysis that provides a guideline for setting thresholds, enabling TTrace to distinguish bug-induced errors from floating-point round-off errors. Experimental results demonstrate that TTrace effectively detects 11 existing bugs and 3 new bugs in the widely used Megatron-LM framework, while requiring fewer than 10 lines of code change. TTrace is effective in various training recipes, including low-precision recipes involving BF16 and FP8.