From 1 January 2020 Chinese citizens (including the citizens of Hong Kong) are granted 7-day visa-free entry to Uzbekistan if they arrive at international airports.
Meanwhile, the citizens of China, including Hong Kong, can stay in Uzbekistan for up to 5 days if they are on a transit stop and depart with an Uzbek national air carrier Uzairways.
If you hold a Chinese passport and wish to travel to Uzbekistan for a longer period, visa is still not an issue. You can apply for an e-visa, which takes 3 days and costs only US$20.