As a rule, air quality standards are set by governments obligated to protect public health and the environment. The specific agency or agencies that set these varies by country or region.
For instance, in the US, the Environmental Protection Agency (EPA) sets and enforces air quality standards. This is done under the Clean Air Act. In the European Union, air quality standards are set by the European Commission and carried out by member states. In China, the Ministry of Ecology and Environment sets air quality standards.
In addition to governments, international organizations provide air quality guidelines. For instance, the World Health Organization (WHO) provides recommendations for countries to improve air quality.
However, guidelines are not the same as standards. Standards are enforceable by law. Guidelines are not.