To determine which option belongs to the category of geophysical hazards, we must first understand what geophysical hazards are. Geophysical hazards are natural phenomena that arise from the dynamic processes of the Earth's physical systems. These often include processes such as earthquakes, volcanic eruptions, tsunamis, and avalanches.

Let's analyze each option given:

1. Infestation: This relates to the multiplication and prevalence of pests or invasive species in an area, leading to environmental damage. It is not a geophysical hazard; rather, it's more connected to biological or ecological concerns.
2. Avalanches: These are masses of snow, ice, and debris falling rapidly down a mountainside. Avalanches are directly related to physical processes and climatic conditions, thus categorizing them as geophysical hazards.
3. Invasive species: These are species that enter new ecosystems and outcompete native species, often leading to ecological imbalance. This is primarily an ecological or environmental hazard, not geophysical.
4. Diseases: This relates to the spread of pathogens among humans, animals, or plants. They fall under biological, rather than geophysical hazards.

Conclusion: The correct answer is Avalanches as they are directly associated with geophysical processes involving terrain and climate. Other options like infestation, invasive species, and diseases are linked to biological or ecological hazards.