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From my naive viewpoint, I would argue that public debt correlates positively with inflation. One cause could be that states with high public debts often use "their" reserve bank (e.g. the Fed) to print money, thus causing an inflation which will reduce the amount of debt by devaluing it.

However, this graphic seems to contradict this:

enter image description here

x axis: public debt, y axis: inflation rate

Is my basic assumption correct? If yes, why does the graphic contradict it?

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The assumption is not necessarily true. For example, many nations with low debt levels (comparable to US or EU) have to often resort to high monetary financing because nobody is willing to lend to them. For example, Zimbabwe (see trading economics data) has debt to GDP below 80% which is quite low by present day standards, yet the country (until just very recently) relied very heavily on monetary financing (see IMF report).

Also, debt to GDP is accumulation of all debt throughout the country's history. A country that in a past run huge budget deficits (and thus needed to get some financing either through monetary or non-monetary means) can now run surplus. It would be more sensible to plot scatterplot of government budget deficit and inflation. There I would expect to see at least some positive correlation.

In addition, inflation does not depend just on supply of money but also demand for money. For example, economic growth will increase demand for money so that is something you would want to control for and there are more important variables to watch out for. In a basic New Keynesian model of money market, the equilibrium is given by:

$$M/P = L(Y,i) \implies P = M/L(Y,i)$$

where $P$ is price level increase in which gives you inflation, $M$ is money supply, $L$ is demand for money that depends on real economic output and interest rates. So even if budget deficit or government debt is financed through increase in money supply it might not necessarily automatically translate itself into inflation as it might be offset by higher demand for money.

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