is knot type invariant under diffeomorphism? Is it possible to have a diffeomorphism of $R^3$ which changes the knot type, for instance the image of a trivial knot is a trefoil knot?

It is well known that the reflection of a trefoil knot is not the same type as the trefoil knot itself. On the other hand any diffeomorphism which preserves orientation can be 
interpolated to the identity through an isotopy... hence it preserves knot type.
Instead diffeomorphism which invert orientation would change the type of chiral knots (as the trefoil knot) but not achiral knots (like the trivial knot). 
