New vaccines have also had a positive impact.
However, diarrhoea is still the fourth-biggest killer of children globally, with almost 500,000 a year dying before their fifth birthday.
This figure could well be a significant under-estimate because of the lack of data in sub-Saharan Africa, where most cases occur.
Preventable and treatable
Diarrhoea is also indirectly responsible for large numbers of deaths, through exacerbating the effects of other diseases, such as pneumonia and measles.
The US researchers, who analysed data from the new Global Burden of Disease study, found well over a third (42%) of deaths happen in Nigeria and India.
Diarrhoeal diseases, such as rotavirus and cholera, are spread by water contaminated with faeces. They are preventable and treatable.
"Diarrhoeal diseases disproportionately affect young children," said lead author Dr Ali Mokdad, from the Institute for Health Metrics and Evaluation at the University of Washington.
"Despite some promising reductions in mortality, the devastating impact of these diseases cannot be overlooked."
Diarrhoea cases in 2015
- 2.39 billion episodes of diarrhoea
- Almost half of those (957.5 million) involved children
- 1.3 million deaths
- Including 499,000 child deaths
- The highest death rates were in Chad and Niger
Source: Lancet
While deaths from diarrhoea have dropped by just over 20% overall, and 34% in children, the rate of infection has been falling far more slowly.
For children it dropped by just over 10% between 2005 and 2015.
Of all the diarrhoeal diseases, rotavirus remains the biggest killer of under-fives, according to this study.
But death rates for the disease were down by 44% in 2015.
The researchers attribute much of this to a relatively new vaccine.
'Unacceptable'
"We're encouraged to see fewer children dying of diarrhoea," said Yael Velleman, senior policy analyst on health and hygiene at WaterAid.
"But it is unacceptable that diarrhoea still claims the lives of nearly half a million children under five each year.
"Up to 50% of under-nutrition is linked to chronic infection, diarrhoea and worm infestation caused by dirty water and poor hygiene."
She said those children's life chances were limited by preventable illness - "all for the lack of conditions we have been taking for granted in the UK for over 100 years".
How to prevent diarrhea
- Access to safe drinking-water
- Improved sanitation
- Hand washing with soap
- Exclusive breastfeeding for the first six months of life
- Good personal and food hygiene
- Education about how infections spread
- Rotavirus vaccination
SOURCE: World Health Organization
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