diff --git a/arch/s390/include/asm/gmap.h b/arch/s390/include/asm/gmap.h
index 5cc46e0dde620..9725586f42597 100644
--- a/arch/s390/include/asm/gmap.h
+++ b/arch/s390/include/asm/gmap.h
@@ -146,7 +146,7 @@ int gmap_mprotect_notify(struct gmap *, unsigned long start,
 
 void gmap_sync_dirty_log_pmd(struct gmap *gmap, unsigned long dirty_bitmap[4],
 			     unsigned long gaddr, unsigned long vmaddr);
-int gmap_mark_unmergeable(void);
+int s390_disable_cow_sharing(void);
 void s390_unlist_old_asce(struct gmap *gmap);
 int s390_replace_asce(struct gmap *gmap);
 void s390_uv_destroy_pfns(unsigned long count, unsigned long *pfns);
diff --git a/arch/s390/include/asm/mmu.h b/arch/s390/include/asm/mmu.h
index bb1b4bef1878b..4c2dc7abc2858 100644
--- a/arch/s390/include/asm/mmu.h
+++ b/arch/s390/include/asm/mmu.h
@@ -32,6 +32,11 @@ typedef struct {
 	unsigned int uses_skeys:1;
 	/* The mmu context uses CMM. */
 	unsigned int uses_cmm:1;
+	/*
+	 * The mmu context allows COW-sharing of memory pages (KSM, zeropage).
+	 * Note that COW-sharing during fork() is currently always allowed.
+	 */
+	unsigned int allow_cow_sharing:1;
 	/* The gmaps associated with this context are allowed to use huge pages. */
 	unsigned int allow_gmap_hpage_1m:1;
 } mm_context_t;
diff --git a/arch/s390/include/asm/mmu_context.h b/arch/s390/include/asm/mmu_context.h
index 929af18b09081..a7789a9f62186 100644
--- a/arch/s390/include/asm/mmu_context.h
+++ b/arch/s390/include/asm/mmu_context.h
@@ -35,6 +35,7 @@ static inline int init_new_context(struct task_struct *tsk,
 	mm->context.has_pgste = 0;
 	mm->context.uses_skeys = 0;
 	mm->context.uses_cmm = 0;
+	mm->context.allow_cow_sharing = 1;
 	mm->context.allow_gmap_hpage_1m = 0;
 #endif
 	switch (mm->context.asce_limit) {
diff --git a/arch/s390/include/asm/pgtable.h b/arch/s390/include/asm/pgtable.h
index 60950e7a25f58..1a71cb19c0891 100644
--- a/arch/s390/include/asm/pgtable.h
+++ b/arch/s390/include/asm/pgtable.h
@@ -566,10 +566,19 @@ static inline pud_t set_pud_bit(pud_t pud, pgprot_t prot)
 }
 
 /*
- * In the case that a guest uses storage keys
- * faults should no longer be backed by zero pages
+ * As soon as the guest uses storage keys or enables PV, we deduplicate all
+ * mapped shared zeropages and prevent new shared zeropages from getting
+ * mapped.
  */
-#define mm_forbids_zeropage mm_has_pgste
+static inline int mm_forbids_zeropage(struct mm_struct *mm)
+{
+#ifdef CONFIG_PGSTE
+	if (!mm->context.allow_cow_sharing)
+		return 1;
+#endif
+	return 0;
+}
+
 static inline int mm_uses_skeys(struct mm_struct *mm)
 {
 #ifdef CONFIG_PGSTE
diff --git a/arch/s390/kvm/kvm-s390.c b/arch/s390/kvm/kvm-s390.c
index 5147b943a864a..db3392f0be212 100644
--- a/arch/s390/kvm/kvm-s390.c
+++ b/arch/s390/kvm/kvm-s390.c
@@ -2631,9 +2631,7 @@ static int kvm_s390_handle_pv(struct kvm *kvm, struct kvm_pv_cmd *cmd)
 		if (r)
 			break;
 
-		mmap_write_lock(current->mm);
-		r = gmap_mark_unmergeable();
-		mmap_write_unlock(current->mm);
+		r = s390_disable_cow_sharing();
 		if (r)
 			break;
 
diff --git a/arch/s390/mm/gmap.c b/arch/s390/mm/gmap.c
index 094b43b121cd5..9233b0acac895 100644
--- a/arch/s390/mm/gmap.c
+++ b/arch/s390/mm/gmap.c
@@ -2549,41 +2549,6 @@ static inline void thp_split_mm(struct mm_struct *mm)
 }
 #endif /* CONFIG_TRANSPARENT_HUGEPAGE */
 
-/*
- * Remove all empty zero pages from the mapping for lazy refaulting
- * - This must be called after mm->context.has_pgste is set, to avoid
- *   future creation of zero pages
- * - This must be called after THP was disabled.
- *
- * mm contracts with s390, that even if mm were to remove a page table,
- * racing with the loop below and so causing pte_offset_map_lock() to fail,
- * it will never insert a page table containing empty zero pages once
- * mm_forbids_zeropage(mm) i.e. mm->context.has_pgste is set.
- */
-static int __zap_zero_pages(pmd_t *pmd, unsigned long start,
-			   unsigned long end, struct mm_walk *walk)
-{
-	unsigned long addr;
-
-	for (addr = start; addr != end; addr += PAGE_SIZE) {
-		pte_t *ptep;
-		spinlock_t *ptl;
-
-		ptep = pte_offset_map_lock(walk->mm, pmd, addr, &ptl);
-		if (!ptep)
-			break;
-		if (is_zero_pfn(pte_pfn(*ptep)))
-			ptep_xchg_direct(walk->mm, addr, ptep, __pte(_PAGE_INVALID));
-		pte_unmap_unlock(ptep, ptl);
-	}
-	return 0;
-}
-
-static const struct mm_walk_ops zap_zero_walk_ops = {
-	.pmd_entry	= __zap_zero_pages,
-	.walk_lock	= PGWALK_WRLOCK,
-};
-
 /*
  * switch on pgstes for its userspace process (for kvm)
  */
@@ -2601,22 +2566,140 @@ int s390_enable_sie(void)
 	mm->context.has_pgste = 1;
 	/* split thp mappings and disable thp for future mappings */
 	thp_split_mm(mm);
-	walk_page_range(mm, 0, TASK_SIZE, &zap_zero_walk_ops, NULL);
 	mmap_write_unlock(mm);
 	return 0;
 }
 EXPORT_SYMBOL_GPL(s390_enable_sie);
 
-int gmap_mark_unmergeable(void)
+static int find_zeropage_pte_entry(pte_t *pte, unsigned long addr,
+		unsigned long end, struct mm_walk *walk)
+{
+	unsigned long *found_addr = walk->private;
+
+	/* Return 1 of the page is a zeropage. */
+	if (is_zero_pfn(pte_pfn(*pte))) {
+
+		/*
+		 * Shared zeropage in e.g., a FS DAX mapping? We cannot do the
+		 * right thing and likely don't care: FAULT_FLAG_UNSHARE
+		 * currently only works in COW mappings, which is also where
+		 * mm_forbids_zeropage() is checked.
+		 */
+		if (!is_cow_mapping(walk->vma->vm_flags))
+			return -EFAULT;
+
+		*found_addr = addr;
+		return 1;
+	}
+	return 0;
+}
+
+static const struct mm_walk_ops find_zeropage_ops = {
+	.pte_entry	= find_zeropage_pte_entry,
+	.walk_lock	= PGWALK_WRLOCK,
+};
+
+/*
+ * Unshare all shared zeropages, replacing them by anonymous pages. Note that
+ * we cannot simply zap all shared zeropages, because this could later
+ * trigger unexpected userfaultfd missing events.
+ *
+ * This must be called after mm->context.allow_cow_sharing was
+ * set to 0, to avoid future mappings of shared zeropages.
+ *
+ * mm contracts with s390, that even if mm were to remove a page table,
+ * and racing with walk_page_range_vma() calling pte_offset_map_lock()
+ * would fail, it will never insert a page table containing empty zero
+ * pages once mm_forbids_zeropage(mm) i.e.
+ * mm->context.allow_cow_sharing is set to 0.
+ */
+static int __s390_unshare_zeropages(struct mm_struct *mm)
+{
+	struct vm_area_struct *vma;
+	VMA_ITERATOR(vmi, mm, 0);
+	unsigned long addr;
+	int rc;
+
+	for_each_vma(vmi, vma) {
+		/*
+		 * We could only look at COW mappings, but it's more future
+		 * proof to catch unexpected zeropages in other mappings and
+		 * fail.
+		 */
+		if ((vma->vm_flags & VM_PFNMAP) || is_vm_hugetlb_page(vma))
+			continue;
+		addr = vma->vm_start;
+
+retry:
+		rc = walk_page_range_vma(vma, addr, vma->vm_end,
+					 &find_zeropage_ops, &addr);
+		if (rc <= 0)
+			continue;
+
+		/* addr was updated by find_zeropage_pte_entry() */
+		rc = handle_mm_fault(vma, addr,
+				     FAULT_FLAG_UNSHARE | FAULT_FLAG_REMOTE,
+				     NULL);
+		if (rc & VM_FAULT_OOM)
+			return -ENOMEM;
+		/*
+		 * See break_ksm(): even after handle_mm_fault() returned 0, we
+		 * must start the lookup from the current address, because
+		 * handle_mm_fault() may back out if there's any difficulty.
+		 *
+		 * VM_FAULT_SIGBUS and VM_FAULT_SIGSEGV are unexpected but
+		 * maybe they could trigger in the future on concurrent
+		 * truncation. In that case, the shared zeropage would be gone
+		 * and we can simply retry and make progress.
+		 */
+		cond_resched();
+		goto retry;
+	}
+
+	return rc;
+}
+
+static int __s390_disable_cow_sharing(struct mm_struct *mm)
 {
+	int rc;
+
+	if (!mm->context.allow_cow_sharing)
+		return 0;
+
+	mm->context.allow_cow_sharing = 0;
+
+	/* Replace all shared zeropages by anonymous pages. */
+	rc = __s390_unshare_zeropages(mm);
 	/*
 	 * Make sure to disable KSM (if enabled for the whole process or
 	 * individual VMAs). Note that nothing currently hinders user space
 	 * from re-enabling it.
 	 */
-	return ksm_disable(current->mm);
+	if (!rc)
+		rc = ksm_disable(mm);
+	if (rc)
+		mm->context.allow_cow_sharing = 1;
+	return rc;
+}
+
+/*
+ * Disable most COW-sharing of memory pages for the whole process:
+ * (1) Disable KSM and unmerge/unshare any KSM pages.
+ * (2) Disallow shared zeropages and unshare any zerpages that are mapped.
+ *
+ * Not that we currently don't bother with COW-shared pages that are shared
+ * with parent/child processes due to fork().
+ */
+int s390_disable_cow_sharing(void)
+{
+	int rc;
+
+	mmap_write_lock(current->mm);
+	rc = __s390_disable_cow_sharing(current->mm);
+	mmap_write_unlock(current->mm);
+	return rc;
 }
-EXPORT_SYMBOL_GPL(gmap_mark_unmergeable);
+EXPORT_SYMBOL_GPL(s390_disable_cow_sharing);
 
 /*
  * Enable storage key handling from now on and initialize the storage
@@ -2685,7 +2768,7 @@ int s390_enable_skey(void)
 		goto out_up;
 
 	mm->context.uses_skeys = 1;
-	rc = gmap_mark_unmergeable();
+	rc = __s390_disable_cow_sharing(mm);
 	if (rc) {
 		mm->context.uses_skeys = 0;
 		goto out_up;
