Your question is not clear. Are you talking about the methodology for quantifying marine pollutants, or are you talking about means of assessing pollution?
In addition, the methodology differs depending on the type of pollutant (microplastics, hydrocarbons, etc.)
As others have said diffuse pollution is a very broad topic and could include nutrients, an array of chemical contaminants entering from dispersed sources or microplastics in the marine environment
Diffuse pollution in the marine environment in the UK has often been commonly associated with nutrients especially nitrogen (DIN) in transitional and coastal water bodies. In this example the overall concentrations of nitrogen- the pressure (and its impacts on ecology such as macro algae- an impact) are monitored. To consider the proportion of nitrogen associated with diffuse sources, source apportionment modelling is then undertaken.
Some background information is here including considerations of understanding the impacts of diffuse pollution (primarily nutrients), on designated sites in the UK which might be of interest...
Indeed, it really depends on the pollutants you want to monitor. A variety of passive sampling techniques have been developed and applied over the years, which can be used to measure organic pollutants but also cationic metals. Passive sampling allows time integrative sampling and includes substantial enrichment meaning that you can measure very low concentrations. For non-polar organic chemicals you can start looking here:
Article Passive Sampling in Regulatory Chemical Monitoring of Nonpol...
For metals, there are other techniques including DGT.