How to allow user to signup providing email address only(updated)

confirmations_controller.rb.diff

--- a/app/controllers/confirmations_controller.rb
+++ b/app/controllers/confirmations_controller.rb
@@ -1,20 +1,19 @@
 class ConfirmationsController < Devise::ConfirmationsController
   def show
     @user = User.find_by_confirmation_token(params[:confirmation_token])
-    if !@user.present?
-      render_with_scope :new
-    end
+    head :not_found unless @user.present?
   end
 
   def confirm_user
-    @user = User.find(params[:user][:confirmation_token])
-    if @user.update_attributes(params[:user]) and @user.password_match?
+    return head :not_found unless params[:user][:confirmation_token].present?
+    @user = User.find_by_confirmation_token(params[:user][:confirmation_token])
+    return head :not_found unless @user.present?
+    if @user.update_attributes(params[:user])
       @user = User.confirm_by_token(@user.confirmation_token)
       set_flash_message :notice, :confirmed
       sign_in_and_redirect("user", @user)
     else
       render :action => "show"
     end
   end
-
 end

devise.rb.diff

--- a/config/initializers/extentions/devise.rb
+++ b/config/initializers/extentions/devise.rb
@@ -1,11 +1,12 @@
 module Devise
   module Models
     module Validatable
-
       def password_required?
-        false
+        return false unless persisted?
+        return true if respond_to?(:confirmed?) && !confirmed?
+        return true if password.present? || password_confirmation.present?
+        return false
       end
-

user.rb.diff

--- a/app/models/user.rb
+++ b/app/models/user.rb
@@ -10,10 +10,4 @@ class User < ActiveRecord::Base


-  
-  def password_match?
-    self.errors[:password] << 'password not match' if password != password_confirmation
-    self.errors[:password] << 'you must provide a password' if password.blank?
-    password == password_confirmation and !password.blank?
-  end
 end