Log files record computational events that reflect system state and behavior, making them a primary source of operational insights in modern computer systems. Automated anomaly detection on logs is therefore critical, yet most established methods rely on log parsers that collapse messages into discrete templates, discarding variable values and semantic content. We propose ContraLog, a parser-free and self-supervised method that reframes log anomaly detection as predicting continuous message embeddings rather than discrete template IDs. ContraLog combines a message encoder that produces rich embeddings for individual log messages with a sequence encoder to model temporal dependencies within sequences. The model is trained with a combination of masked language modeling and contrastive learning to predict masked message embeddings based on the surrounding context. Experiments on the HDFS, BGL, and Thunderbird benchmark datasets empirically demonstrate effectiveness on complex datasets with diverse log messages. Additionally, we find that message embeddings generated by ContraLog carry meaningful information and are predictive of anomalies even without sequence context. These results highlight embedding-level prediction as an approach for log anomaly detection, with potential applicability to other event sequences.