Visitor pattern for const and nonconst versions of a tree

I am stuck with a code duplication issue, regarding the visitor pattern for a tree. The current situation is as follows: I have a tree, consisting of two different node classes, i.e. leafs and non-leafs. In addition I have two visitor base classes that look very alike except that one visits const trees and the other non-const trees. The actual actions the concrete visitors have to do are independent of the node's concrete types. I'll give a short example:

class Visitor;
class ConstVisitor;

class Node {
public:
  virtual void accept(Visitor&) = 0;
  virtual void accept(ConstVisitor&) const = 0;
};

class Leaf : public Node {
  virtual void accept(Visitor& v)        {v.visitLeaf(*this);}
  virtual void accept(ConstVisitor& cv)  {cv.visitLeaf(*this);}
};

class CompoundNode : public Node {
public:
  vector<Node*> getChildren() const;
  virtual void accept(Visitor& v)        {v.visitCompoundNode(*this);}
  virtual void accept(ConstVisitor& cv)  {cv.visitCompoundNode(*this);}
};

class Visitor {
protected:
  virtual void processNode(Node& node) = 0;
public:
  void visitLeaf(Leaf& leaf) {
    processNode(leaf);
  }
  void visitCompoundNode(CompoundNode& cNode) {
    processNode(cNode);
    auto children = cNode.getChildren();
    for (auto child : children)
      child->accept(this);
  }
};

class ConstVisitor {
protected:
  virtual void processNode(Node const& node) = 0;
public:
  void visitLeaf(Leaf const& leaf) {
    processNode(leaf);
  }
  void visitCompoundNode(CompoundNode const& cNode) {
    processNode(cNode);
    auto children = cNode.getChildren();
    for (auto child : children)
      child->accept(this);
  }
};

Concrete visitor classes inherit either from Visitor or from ConstVisitor, depending on whether their processNode method has to alter the nodes visited or not.

You see, there is lots of code duplication betwee