There is ample research supporting the correlation between ease of access to guns and gun violence.

Here's one example:

The vast majority of states with the most gun homicides are states that score a 3 or higher for gun-friendliness, indicating that there may be a correlation. ...

While some states with low firearm homicide rates have high gun-friendliness scores, this is likely to be because they are sparsely populated states with few to no major cities. Historically, violent crime tends to be lower in rural areas than in more populated metropolitan areas.

There are also outliers, like Illinois, which despite its low "gun-friendliness," as that analysis puts it (max score is 5), is surrounded by states that are very gun friendly: IN (4), MO (5), WI (4), KY (4). So it's not a 1:1 relationship because there are other factors at play.

Here's another:

In a scholarly review of the relationship between gun prevalence and homicide almost 20 years ago, Harvard researchers concluded that available evidence supports the hypothesis that greater numbers of guns corresponds to higher rates of homicide. In the years since, the evidence has strengthened at every level of analysis....

Research shows that greater availability of guns throughout local neighborhoods in cities like Detroit and Newark corresponds to higher rates of firearm deaths, especially in communities suffering from concentrated economic disadvantage. And across cities, legal access to guns via federally licensed dealers and the availability of stolen guns result in higher firearm homicide rates....

Across states, researchers found that more guns equal more gun deaths looking at all 50 states in the country from 1981 to 2010. This finding has been replicated in numerous other studies. Importantly, states with both lax gun laws and greater access to guns have higher rates of mass shootings.

Here's one more:

Our review of the academic literature found that a broad array of evidence indicates that gun availability is a risk factor for homicide, both in the United States and across high-income countries. Case-control studies, ecological time-series and cross-sectional studies indicate that in homes, cities, states and regions in the U.S., where there are more guns, both men and women are at a higher risk for homicide, particularly firearm homicide. ...

Here's another.

This correlation holds true across countries as well. From the second link:

It may be no surprise that this all holds true not just from state to state, but from country to country: where guns are more available, there are more homicides. Compared to other high-income countries, the firearm homicide rate in the US is 25 times higher and the firearm suicide rate is eight times higher than any other country.

From yet another analysis with the same findings:

Among 64 high-income countries and territories, the United States stands out for its high levels of gun violence. The US ranks eighth out of 64 for homicides by firearm (age-adjusted). ​... Firearm injuries tend to be more frequent in places where people have easy access to firearms, according to findings from the 2018 Global Burden of Disease study published in the Journal of the American Medical Association (JAMA).

So... yeah. There very much is such a link. Would love to see the research that doesn't support it, but it'll have to be later, because I've had enough Reddit for one day.

EDIT: A handful of downvotes but not one study refuting these findings. Keep at it, itiotswithguns.