diff --git a/.changeset/fiery-turkeys-travel.md b/.changeset/fiery-turkeys-travel.md
new file mode 100644
index 00000000..aca5d6c6
--- /dev/null
+++ b/.changeset/fiery-turkeys-travel.md
@@ -0,0 +1,5 @@
+---
+'@css-modules-kit/core': minor
+---
+
+feat!: remove unused `isAbsolute`
diff --git a/.changeset/orange-readers-report.md b/.changeset/orange-readers-report.md
new file mode 100644
index 00000000..2218a068
--- /dev/null
+++ b/.changeset/orange-readers-report.md
@@ -0,0 +1,5 @@
+---
+'@css-modules-kit/core': patch
+---
+
+fix: report "Cannot import module" diagnostic for unresolvable bare specifiers
diff --git a/.changeset/some-rules-stick.md b/.changeset/some-rules-stick.md
new file mode 100644
index 00000000..e4b9e9ee
--- /dev/null
+++ b/.changeset/some-rules-stick.md
@@ -0,0 +1,5 @@
+---
+'@css-modules-kit/core': patch
+---
+
+fix: return `undefined` for non-existent CSS module paths in resolver
diff --git a/packages/codegen/e2e-test/index.test.ts b/packages/codegen/e2e-test/index.test.ts
index c96db94c..86eb9321 100644
--- a/packages/codegen/e2e-test/index.test.ts
+++ b/packages/codegen/e2e-test/index.test.ts
@@ -12,7 +12,7 @@ test('generates .d.ts', async () => {
   const iff = await createIFF({
     'src/a.module.css': dedent`
       @import './b.module.css';
-      @import './external.css';
+      @import './unmatched.module.css';
       /* @import '@/c.module.css'; */ /* TODO: Fix this */
       .a1 { color: red; }
     `,
@@ -26,8 +26,10 @@ test('generates .d.ts', async () => {
       // @ts-expect-error
       styles.a2;
     `,
+    'src/unmatched.module.css': '',
     'tsconfig.json': dedent`
       {
+        "exclude": ["unmatched.module.css"],
         "compilerOptions": {
           "lib": ["ES2015"],
           "noEmit": true,
@@ -47,6 +49,7 @@ test('generates .d.ts', async () => {
     declare const styles = {
       a1: '' as readonly string,
       ...(await import('./b.module.css')).default,
+      ...(await import('./unmatched.module.css')).default,
     };
     export default styles;
     "
diff --git a/packages/core/src/checker.test.ts b/packages/core/src/checker.test.ts
index e7d8d289..a21a4b7f 100644
--- a/packages/core/src/checker.test.ts
+++ b/packages/core/src/checker.test.ts
@@ -223,7 +223,6 @@ describe('checkCSSModule', () => {
     });
     const check = prepareChecker();
     const diagnostics = check(readAndParseCSSModule(iff.paths['a.module.css'])!);
-    // TODO: Report diagnostics for `package/c.module.css`
     expect(formatDiagnostics(diagnostics, iff.rootDir)).toMatchInlineSnapshot(`
       [
         {
@@ -236,6 +235,16 @@ describe('checkCSSModule', () => {
           },
           "text": "Cannot import module './b.module.css'",
         },
+        {
+          "category": "error",
+          "fileName": "<rootDir>/a.module.css",
+          "length": 20,
+          "start": {
+            "column": 10,
+            "line": 2,
+          },
+          "text": "Cannot import module 'package/c.module.css'",
+        },
         {
           "category": "error",
           "fileName": "<rootDir>/a.module.css",
@@ -246,6 +255,16 @@ describe('checkCSSModule', () => {
           },
           "text": "Cannot import module './b.module.css'",
         },
+        {
+          "category": "error",
+          "fileName": "<rootDir>/a.module.css",
+          "length": 20,
+          "start": {
+            "column": 18,
+            "line": 4,
+          },
+          "text": "Cannot import module 'package/c.module.css'",
+        },
       ]
     `);
   });
diff --git a/packages/core/src/checker.ts b/packages/core/src/checker.ts
index 7c545246..ee86b3de 100644
--- a/packages/core/src/checker.ts
+++ b/packages/core/src/checker.ts
@@ -10,7 +10,7 @@ import type {
   Resolver,
   TokenImporter,
 } from './type.js';
-import { isValidAsJSIdentifier } from './util.js';
+import { isURLSpecifier, isValidAsJSIdentifier } from './util.js';
 
 export interface CheckerArgs {
   config: CMKConfig;
@@ -39,13 +39,15 @@ export function checkCSSModule(cssModule: CSSModule, args: CheckerArgs): Diagnos
   }
 
   for (const tokenImporter of cssModule.tokenImporters) {
+    if (isURLSpecifier(tokenImporter.from)) continue;
     const from = args.resolver(tokenImporter.from, { request: cssModule.fileName });
-    if (!from || !args.matchesPattern(from)) continue;
-    const imported = args.getCSSModule(from);
-    if (!imported) {
+    if (!from) {
       diagnostics.push(createCannotImportModuleDiagnostic(cssModule, tokenImporter));
       continue;
     }
+    if (!args.matchesPattern(from)) continue;
+    const imported = args.getCSSModule(from);
+    if (!imported) throw new Error('unreachable: `imported` is undefined');
 
     if (tokenImporter.type === 'value') {
       const exportRecord = args.getExportRecord(imported);
diff --git a/packages/core/src/index.ts b/packages/core/src/index.ts
index cd93577d..fbe18ca5 100644
--- a/packages/core/src/index.ts
+++ b/packages/core/src/index.ts
@@ -36,6 +36,6 @@ export {
 } from './file.js';
 export { checkCSSModule, type CheckerArgs } from './checker.js';
 export { createExportBuilder } from './export-builder.js';
-export { join, resolve, relative, dirname, basename, parse, isAbsolute } from './path.js';
+export { join, resolve, relative, dirname, basename, parse } from './path.js';
 export { findUsedTokenNames } from './util.js';
 export { convertDiagnostic, convertDiagnosticWithLocation, convertSystemError } from './diagnostic.js';
diff --git a/packages/core/src/path.ts b/packages/core/src/path.ts
index 8302dd12..18b3c1f0 100644
--- a/packages/core/src/path.ts
+++ b/packages/core/src/path.ts
@@ -32,6 +32,3 @@ export function parse(path: string): ParsedPath {
   const { root, dir, base, name, ext } = nodePath.parse(path);
   return { root: slash(root), dir: slash(dir), base, name, ext };
 }
-
-// eslint-disable-next-line @typescript-eslint/unbound-method
-export const isAbsolute = nodePath.isAbsolute;
diff --git a/packages/core/src/resolver.test.ts b/packages/core/src/resolver.test.ts
index 70563816..40e8d8ba 100644
--- a/packages/core/src/resolver.test.ts
+++ b/packages/core/src/resolver.test.ts
@@ -32,8 +32,7 @@ describe('createResolver', async () => {
     const resolve = createResolver(normalizeCompilerOptions({}, iff.rootDir), undefined);
     expect(resolve('./a.module.css', { request })).toBe(iff.paths['a.module.css']);
     expect(resolve('./dir/a.module.css', { request })).toBe(iff.paths['dir/a.module.css']);
-    // FIXME: It should return `undefined`.
-    expect(resolve('./non-existent.module.css', { request })).toBe(iff.join('non-existent.module.css'));
+    expect(resolve('./non-existent.module.css', { request })).toBe(undefined);
   });
   describe('resolve with `paths` option', () => {
     test('basic', () => {
diff --git a/packages/core/src/resolver.ts b/packages/core/src/resolver.ts
index 1bb88e04..d4aa9f4f 100644
--- a/packages/core/src/resolver.ts
+++ b/packages/core/src/resolver.ts
@@ -1,16 +1,13 @@
-import { fileURLToPath, pathToFileURL } from 'node:url';
 import type { CompilerOptions } from 'typescript';
 import ts from 'typescript';
-import { isAbsolute, resolve } from './path.js';
+import { resolve } from './path.js';
 import type { Resolver, ResolverOptions } from './type.js';
 
 export function createResolver(
   compilerOptions: CompilerOptions,
   moduleResolutionCache: ts.ModuleResolutionCache | undefined,
 ): Resolver {
-  return (_specifier: string, options: ResolverOptions) => {
-    let specifier = _specifier;
-
+  return (specifier: string, options: ResolverOptions) => {
     const host: ts.ModuleResolutionHost = {
       ...ts.sys,
       fileExists: (fileName) => {
@@ -29,27 +26,8 @@ export function createResolver(
     );
     if (resolvedModule) {
       // TODO: Logging that the paths is used.
-      specifier = resolvedModule.resolvedFileName.replace(/\.module\.d\.css\.ts$/u, '.module.css');
-    }
-    if (isAbsolute(specifier)) {
-      return resolve(specifier);
-    } else if (isRelativeSpecifier(specifier)) {
-      // Convert the specifier to an absolute path
-      // NOTE: Node.js resolves relative specifier with standard relative URL resolution semantics. So we will follow that here as well.
-      // ref: https://nodejs.org/docs/latest-v23.x/api/esm.html#terminology
-      return resolve(fileURLToPath(new URL(specifier, pathToFileURL(options.request)).href));
-    } else {
-      // Do not support URL or bare specifiers
-      // TODO: Logging that the specifier could not resolve.
-      return undefined;
+      return resolve(resolvedModule.resolvedFileName.replace(/\.module\.d\.css\.ts$/u, '.module.css'));
     }
+    return undefined;
   };
 }
-
-/**
- * Check if the specifier is a relative specifier.
- * @see https://nodejs.org/docs/latest-v23.x/api/esm.html#terminology
- */
-function isRelativeSpecifier(specifier: string): boolean {
-  return specifier.startsWith('./') || specifier.startsWith('../');
-}
diff --git a/packages/core/src/util.ts b/packages/core/src/util.ts
index a0676fcf..c55828a6 100644
--- a/packages/core/src/util.ts
+++ b/packages/core/src/util.ts
@@ -25,3 +25,7 @@ export function findUsedTokenNames(componentText: string): Set<string> {
   }
   return usedClassNames;
 }
+
+export function isURLSpecifier(specifier: string): boolean {
+  return URL.canParse(specifier);
+}