Process cubes play a crucial role in multi-dimensional process mining by extending the capabilities of traditional process mining approaches. Here's how they differ and what they bring to the table:

1. **Multi-dimensional Analysis**: Traditional process mining focuses on the control-flow perspective, i.e., the sequence of activities. Process cubes, however, allow for the analysis of processes from multiple dimensions, such as time, resources, data, and other organizational aspects. This multi-dimensional view provides a more comprehensive understanding of processes.

2. **OLAP Operations**: Process cubes leverage Online Analytical Processing (OLAP) operations like roll-up, drill-down, slice, and dice. These operations enable users to interact with process data at different levels of granularity and from different angles. For instance, users can drill down to see detailed data or roll up to see aggregated data.

3. **Contextual Insights**: By incorporating various dimensions, process cubes provide contextual insights. For example, they can help answer questions like "How does the process differ between regions?" or "How has the process changed over time?" Traditional process mining may not capture these contextual nuances.

4. **Comparative Analysis**: Process cubes facilitate comparative analysis. Users can compare process variants based on different dimensions, such as comparing the process for different customer groups or different time periods.

5. **Performance Analysis**: Process cubes can integrate performance metrics, allowing users to analyze not just the sequence of activities but also their performance. This could include metrics like throughput time, cost, or resource utilization.

Here's a simple breakdown of the differences:

|   | Traditional Process Mining | Multi-dimensional Process Mining with Process Cubes |
|---|---|---|
| **Perspective** | Control-flow (activity sequence) | Multiple dimensions (time, resources, data, etc.) |
| **Interaction** | Static views | Interactive OLAP operations (roll-up, drill-down, slice, dice) |
| **Context** | Limited context | Rich contextual insights |
| **Comparison** | Limited comparative analysis | Facilitates comparative analysis |
| **Performance** | May not integrate performance metrics | Can integrate and analyze performance metrics |

In summary, process cubes in multi-dimensional process mining provide a more holistic, interactive, and context-aware approach to understanding and analyzing processes compared to traditional process mining techniques.